9 cards are selected with replacement from a standard pack of 52 cards with 12 picture, 20 odd and 20 even cards.
a)How many different sequences of 9 cards are possible?
b)How many of the sequences in part (a) will contain 4 picture cards,3 odd and 2 even cards?
For part a) it will be 9 spaces all of which have 52 possibilities, so 52^9.
For part b) it will be 12^4 x 20^3 x 20^2. But the picture cards can be arranged so that the picture isnt just in the first 3 positions and the odd and even to be in other positions also.
So, the number of sequences will be 12^4 x 20^3 x 20^2 x 9!/(4!3!2!).
If there is a mistake or you have something to add to the logic I used, please help.