76. Distribution problems (category 7)

[@AmitKhuranaSir]

At 52:04 I have done a small mistake for exactly 9 toys number of ways should 10C9 * 2^1 that is 20 ways but I have written only 2 ways....

[@manishrai8136]

at 52:54

[@guyswapnil]

Sir why are we not arranging the 9 toys which we are selecting to give to children A

[@arbajkhan042]

Sir i think 10C9*3^1 is right answer Correct me if I am wrong

[@mrutyunjayapradhan3599]

@@arbajkhan042 no bro it's 10C9 2^1

[@rounakshaw3052]

@@guyswapnil because the order doesn't matter here, it does not matter whether you give toy A first or toy B first. Eventually, all 9 toys were handed over to child A.

[@namantanwar5078]

Identical balls in Identical boxes maine kahi nahi dekha, even after solving so many questions, this topic is missing from almost every resource. Gate 2022 mai iska question aagaya tha surprisingly, thank you so much for these exhaustive lectures sir!

[@sumanghosh6203]

10c9 * 2(to the power 1) + 10c10 * 2(to the power zero) = 21

[@shamshuddinshaik2218]

Greatly covered...wide range concepts and questions...tnq so much sir...exhaustive teavhing hai apka....💖❤💖❤

[@AmitKhuranaSir]

Hi... Please share my channel with your friends also.... Here is the link... kzbin.info

[@erpankajgyan1120]

2022 me gate cse paper me identical to identical aya tha Apke wala Kai teacher nahi padhaya es topic

[@strangebrew1]

SIr padhai mein itna maza kabhi nahi aaya, jitna aapke lectures sunne mein aata hai.

[@ajaybanshkar55]

15:10 You are doing great jobs sir, specially those who has slow learning & has hesitation in class of 200 students.

[@tejasdongare2953]

This question At 74:4 can also be done as 30C11* 19C11 / 2 both gives same answer

[@chaitanyapaigude8094]

same approach bro

[@rhythmbhandari1700]

Congo sir i saw first time ads on ur channel aapka channel monitize ho gyaa 🤩

[@AmitKhuranaSir]

Thanks..... Btw It's already monetized from 1 year....

[@rhythmbhandari1700]

@@AmitKhuranaSir that's even great 💯💯💯💯

[@surajsharma-1554]

Another approach for 1:23 can be to imagine 3 groups having 11,11 and 8 players!

[@vivekjangir629]

sir plz clarify this doubt: at timestamp 28:56 you are solving it by non negative integral solution, but the toys are not identical here

[@ajaybanshkar6680]

1:26:00 4 Toys distribute into 3 identical boxes : 4!/(1!1!2!*2!) is it right answer?

[@atharvacharde5628]

22:30 sir vaha pe 3! se multiply krna padega na sir quki distribute bola hai to 343,433,334 ... ye sab alag alag honge na sir and sir divide by 2! karna padega na sir as group of 3 3 toys are repeated

[@taneyasoni]

sending u love and respect sir.

[@abhishekchaudhary6554]

Sir at 1:20:20 , I did the question as (30 C 11) * (19 C 11). Please let me know that if this approach is correct or not. I solved it using the Combination problem approach. Since, order in the team does not matter thus it is a combination problem and not a Permutation problem. Please reply sir !!

[@aaakaaash9316]

excellent chaudhary only a small mistake that u have to divide it by 2! becoz reason is very simple in 30C11 u can take one set of 11 players and in 19C11 u can take another set of 11 players right but the sets can arrange themselves in 2! ways also...and we have already specified about identical teams... so ordering is immaterial in such case... for Q2. (30 C 11) * (19 C 11) this is correct when the teams r specified of labeled... that is for team A and Team B so the arrangement of teams are important in such case...

[@chaitanyapaigude8094]

@@aaakaaash9316 Thankyou bro

[@rithikvishwakarma1644]

39:13 i have doubt can any one solve...? We have 4 toys and we need to distribute among 3 children and every child must have at least 1 toy. So first we give each child 1 toy First child has 4 ways 2nd child has 3 ways 3rd child has 2 ways Total ways to distribute 1 toy to each child are 4×3×2. Now we remained 1 toy which has 3 choices so ans should be 4×3×2×3 Please help

[@RitikRaushan-hh1pj]

@AmitKhuranaSir same doubt

[@sarth8065]

These two are different questions. The one which sir have described is : 1) Number of ways in which we can distribute 4 toys to 3 children. The approach you have followed is the answer of : 2) After distributing 1 toy to each, how many ways are there to distribute the remaining toys.

[@chaitanyapaigude8094]

1:23:16 sir my approach was (30c11*19c11)/2! is it correct too?

[@mohdzaheenafzal5103]

no of arrangement of 3 identical balls in 3 identical bins sir ye kis type ki problem hai (gate 2022) question ,maine abhi lecture 75 tak kar liye hain please reply sir

[@AmitKhuranaSir]

See end of this video....

[@abhinav1116]

1:18:15 sir 0 is coming 2 times why we didn't take 2!

[@sundarIIITian]

Same doubt someone clarify 🥲

[@rockybalboa6969]

zero is value is of no use it would not be taken

[@harshilshah8983]

(4,0,0) ek hi baar aaya hai. 4!/4! bhi 1 hi hota hai. Toh that way humein 2! se devide nahi karna padega. That means 0! ki koi importance nai hai yaha.

[@trojanhorse8278]

@1:21:50 why it's UOP? Team 1 and Team 2 both are different and it does matter which players are chosen for which team so it should be OP case. Unlike groups by default it's assumed that two teams are different since they'll compete with each other so I think that it's not necessary to specify they are distinct. Can u please confirm, Or where i'm making a mistake ?

[@rockybalboa6969]

it is not specified which as team A and Team B

[@thokchomphalgunisingh2199]

but by default we assume they are identical in combinatorics?@@rockybalboa6969

[@Gate2025-jy6oz]

Thanks @AmitKhuranaSir great lecture but At 1:00:37 , it is wrong it should also be divided by 3! because of 3 identical groups 😅 how i have done it , by learning from you only and breakdowing the problem and from next two problems ❤

[@tashilamo8539]

1:14:50 check this part out you'll know why we did not divide it by 3!

[@tashilamo8539]

Just rewind few seconds before the above mentioned time

[@thokchomphalgunisingh2199]

why the question "&t= 1:20:00" is UOP? 2 teams should be treated as distinct in combinatorics

[@MEMER4UONLY]

sir @1:18:16 0 is coming two times so why we are not dividing by 2!

[@bhanupratap-qj4lp]

Please reply sir for above query

[@BhanuPratap-ht8vm]

@31:32 sir in one and you did 66 and in another and it is 3^10 which one is correct?I am confused sir.... meanwhile thankyou sir for providing such beautiful lectures 🙂🙂

[@alokbaidya1247]

66 is for distributing 10 IDENTICAL toys between 3 children, while 3^10 is for distributing 10 toys(All toys are distinct) between 3 children.

[@alokbaidya1247]

@Rounak Shaw 👍

[@Abhinav-d3z]

Thank you sir for these beauty❤

[@abhishekchoudhury3328]

new tripod for the lecture.

[@conceptisthekey5643]

Sir one doubt at 25:00 ke sir hmm jab distribute 10 toys among 3 children kar rhae hai such that 1st child gets 3 and 2nd gets 4 and 3rd gets 3 toh sir select krke dena toh samjh ayya pr sir 3! se multiply nhi hogi kyuki children ko 1st 2nd 3rd numbering dene ke liye bhi toh 6 ways hongae.Plz clear my doubt sir.

[@ViralAlucard]

I think the orders are fixed in the distribution like when we have mentioned explicitly ascending order or descending order in permutation problem then we have only one way and in such cases we only multiply my 1! rather than using r! . Its my assumptions only.

[@than0s869]

Sir can you tell me this question answer :- The number of arrangements of six identical balls in three identical bins is ___________ My answer is 7 , Love you sir🥰

[@GateCse-2025]

bhai maine tumhara channel dekha phle mai bhi minecraft bhot khelta tha...😂 or kya raha gate ka result?

[@than0s869]

@@GateCse-2025 sorry brother but i am not preparing for gate. 😃

[@GateCse-2025]

@@than0s869 Okay..!

[@than0s869]

@@GateCse-2025 whay about you?

[@GateCse-2025]

@@than0s869 2025 will gonna be my first attempt. let's see.

[@shaikchanmehboob7958]

53:02 ans is 21 ways na sir?

[@rockybalboa6969]

yes

[@abhishekchoudhury3328]

thank you sir !

[@rajukachori9536]

what is the formula of identity to distinct in home work question 2 at 1:26:10

[@sunilpatidar8609]

sir distribute 10 toys bw 3 children sir apne toys ko identical kyu let kiya apne bola tha jab tk bola na jaye distinct let krna

[@AmitKhuranaSir]

Please mention timestamp of video....

[@sunilpatidar8609]

@@AmitKhuranaSir sir groups ko by default identical hi assume krna hai na in distrubutive problem

[@AmitKhuranaSir]

@@sunilpatidar8609 no we have to take them as different... Rest depends on options in question....

[@AmitKumar-dt8vp]

@@AmitKhuranaSir 29:15

[@codeb3nder862]

At 52:04, exactly 9 should be 20 toys?

[@AmitKhuranaSir]

I am not getting your doubt.... Please explain it little more....

[@codeb3nder862]

@@AmitKhuranaSir In "exactly 9" question, it should be 10C9 x 2 = 20.

[@AmitKhuranaSir]

@@codeb3nder862 Yes you are correct I have done a small mistake here.... Thanks for identifying that....

[@vidyamishra5195]

Thankyou thankyou thankyou so much sir

[@kadharhussan1940]

Sir @38:56 duplicates were occured so we need to divide by 2!

[@Thakur_Abhays]

It is not like that what you are thinking It is sol of 5c3*2c1*1c1 previously sir has covered it. What you are saying it will happen in distinct to identical case

[@keerthigvkp8248]

Could u pls explain it some more clrly

[@fneful]

24:25 sir 10 toys ke 3 group of size (3,4,3) bola hai, lekin sir isme 2 group same size of 3 ka hai toh 2! se extra divide nahi hoga ?

[@rockybalboa6969]

thats only for UOP

[@shefali9554]

39:10 so according to that solution there are 36 ways to distribute. How sir. I can only see 3 ways to distribute

[@cosmophile8218]

12 ways se 2 1 1 toys distribute kiye ja sakte hain t1 t2 t3 t4

[@dhruvpurohit5485]

43:55 child A ko Goli Mari 😂😂

[@mrutyunjayapradhan3599]

Thankyou sir 🙏🏻

[@than0s869]

Nice sir you are op😘🥰

[@cuberkingbro]

love you sir ❣❣❣❣

[@ashakumari7106]

Sir at. 1:22:30 . I think i select 11from 30 then 11 from 19 and then divide by factorial 2 30c11*19c11/2! Is it right sir

[@prasadpathak3658]

I also have done it in the same way

[@harshilshah8983]

Yes it is also correct.

[@rachnapanigrahi139]

can you explain why have you divided it by 2! here

[@guy.with.moustache]

​@@rachnapanigrahi139have you got the answer to this

[@nafeesshaikh310]

At 39 I think you did a mistake, 4!/1!*1!*2! You forgot to divide 2! as we have two times 1!

[@AmitKhuranaSir]

39:00 This is OP and not UOP In UOP we have to divide by 2!

[@nafeesshaikh310]

@@AmitKhuranaSir ok sir got it

[@kadharhussan1940]

@@AmitKhuranaSir thanks sir my doubt is solved

[@cuberkingbro]

love from hyderabad sir

[@sumitdohan549]

👍

[@AK-dg4hk]

💯⚘🙏

[@rithikvishwakarma1644]

why the ans is not 10C9 * 3 because Chilld 1 atleast 9 and remained one toy has three choices. @AmitKhuranaSir