Question

How many ways are there to distribute:

a.) 20 identical lollipops to 4 children

b.) 20 different toys to the 4 children

c) 20 different toys to the 4 children if each child gets exactly 5 toys

Answer 1

a)

The total number of ways to distribute n identical lollipops among r children are

Here, n = 20 , r = 4 ,

Hence , total number of ways = = = 969

b) As there are 20 different toys which are to be distributed among 4 children,

So, each child can get 20 toys.

Hence ,by multiplication principle ,

Total number of ways = (20)(20)(20)(20) = 20⁴ = 160,000

C) As each child must get exactly 5 toys ,

5 toys will be distributed to 1st child by = 15504 ways

Remaining 15 toys will be distributed to 2nd child by = 3003 ways.

Remaining 10 toys will be distributed to 3rd child by = 252 ways

& Last child will get remaining 5 toys by = 1 way.

& Also selection of child is done by 4 ways.

Hence ,total number of ways = 4 (15504+3003+252+1) = 75,040