Here is the question:
In how many different ways can you draw a card (without return) so that your cards have exactly two aces and two red cards? (deck of cards has 52 cards in total with 26 red cards and 26 black cards, 2 of the red cards are aces and 2 of the black cards are aces.)
(a) when drawing 4 cards
(b) when drawing 5 cards
(c) when drawing 6 cards
(d) when drawing 7 cards
*order does matter
My approach to the question is first to find/split possible cases, for example for (a): i can draw 2 red aces and then 2 black not aces, or one red ace, one black ace, one red not ace, one black not ace or 2 black aces and 2red not aces.
Then for solving this i was thinking: $C(4,2)*2*24*23 + C(4,1)*2*C(3,1)*2*C(2,1)*24^2+C(4,2)*2*24*23$
Is my approach to the question correct?