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 = [tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]
The number of ways of selecting the first 4 crayons for first child = [tex]^{12}C_4=\dfrac{12!}{4!(12-4)!}=\dfrac{12\times11\times10\times9\times8!}{(24)\times 8!}\\\\=495[/tex]
Colors left = 12-4 =8
Now, the again selecting 4 colors out of 8 for second child = [tex]^{8}C_4=\dfrac{8!}{4!(8-4)!}=\dfrac{8\times7\times6\times5\times4!}{(24)\times4!}=70[/tex]
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.
