Permutations and combinations

Question

In how any ways can 8 different shirts be distributed among 4 different people so that each recieves 2 shirts?

Comments

105?

Answer 1

P1 + P2 + P3 + P4 = 8

2       2      2        2   

 

number of solution is given by   $\binom{n+r-1}{r}$

n=4 , r= 8

$\binom{4+8-1}{8}$

= $\binom{11}{8}$  =165 ??

Comments

This is the case of n distinct objects to be assigned to n distinct  groups.So,first person needs to select 2 shirts from 8 different shirts ,then the 2nd person needs to select 2 shirts from 6 remaining shirts and the process goes on .So,the answer is 8C2 * 6C2* 4C2* 2C2=2520.

Answer 2

This is the case of n distinct objects to be assigned to n distinct  groups.So,first person needs to select 2 shirts from 8 different shirts ,then the 2nd person needs to select 2 shirts from 6 remaining shirts and the process goes on .So,the answer is 8C2 * 6C2* 4C2* 2C2=2520.

Answer 3

so there is a direct formula which can be applied here m^n-m, where m is number of persons and n is different objects
4^8-4=65532

ps. if my answer is right i ll  explain the formula otherwise ignore