Question

How many ways are there to distribute three different teddy bears and nine identical lollipops to four children (a) Without restriction? (b) With no child getting two or more teddy bears? (c) With each child getting three ""goodies""?

Answer 1

Answer: a) 14080, b) 5280, c) 64.

Explanation:

Since we have given that

Number of teddy bears = 3

Number of identical lollipops = 9

Total number of things = 3+9 =12

Number of children = 4

(a) Without restriction?

Number of ways would be

`4^3* ^(12)C_3\\\\=14080`

(b) With no child getting two or more teddy bears?

`4* 3!* ^(12)C_9\\\\=5280`

(c) With each child getting three ""goodies""?

`4^3=64`

Hence, a) 14080, b) 5280, c) 64.