Question

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

child to play with, then another 4 are given to a second child to play with, and finally
the last 4 are given to a third child. In how many was can these crayons be
distributed?

Answer 1

Answer: 34,560

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=(n!)/(r!(n-r)!)`

The number of ways of selecting the first 4 crayons for first child =
`^(12)C_4=(12!)/(4!(12-4)!)=(12*11*10*9*8!)/((24)* 8!)\\\\=495`

Colors left = 12-4 =8

Now, the again selecting 4 colors out of 8 for second child =
`^(8)C_4=(8!)/(4!(8-4)!)=(8*7*6*5*4!)/((24)*4!)=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.