Question

A box of crayons has 12 different coloured crayons in it. 4 crayons are given to one

Answer 1

Answer:   34,560

Step-by-step explanation:

Total crayons of different color = 12

Total children = 3

Each child will get 4 crayons.

Number of combinations of selecting r things out of n things = $^nC_r=\dfrac{n!}{r!(n-r)!}$

The number of ways of selecting the first 4 crayons for first child = $^{12}C_4=\dfrac{12!}{4!(12-4)!}=\dfrac{12\times11\times10\times9\times8!}{(24)\times 8!}\\\\=495$

Colors left = 12-4 =8

Now, the again selecting 4 colors out of 8 for second child = $^{8}C_4=\dfrac{8!}{4!(8-4)!}=\dfrac{8\times7\times6\times5\times4!}{(24)\times4!}=70$

Colors left =4

Number of ways of selecting 4 colors out of 4 for third child  =1

Total number of ways = 495 x 70 x 1 = 34650   [By fundamental principle of counting]

Hence, the total number of ways = 34,560.