Solution given:- There are 4 aces, 4 king and 4 jacks and their selection can be made in the following ways:

^{12}C

_{1} X

^{8}C

_{1} X

^{4}C

_{1} = 12 X 8 X 4.

Total selections can be made =

^{52}C

_{3}= 52 X 51 X 50.

Therefore required probability = $\displaystyle \frac{(12)(8)(4)}{ (52)(51)(50)}$

I don't understand why are we taking

^{12}C

_{1} X

^{8}C

_{1} X

^{4}C

_{1} = 12 X 8 X 4 instead of

^{4}C

_{1} X

^{4}C

_{1} X

^{4}C

_{1} = 4 x 4 X 4 for the numerator. Since, we are selecting 1 ace from 4 aces, 1 king from 4 kings and 1 jack from 4 jacks shouldn't we be taking

^{4}C

_{1} X

^{4}C

_{1} X

^{4}C

_{1} = 4 x 4 X 4 for the favourable events ? Please advice on the above.

Thanks in advance !