A stack of cards contains four Aces three Kings two Queens a

A stack of cards contains four Aces, three Kings, two Queens and six other cards which are different. Seven cards are randomly drawn from the stack, without replacement.

Find the probability that the drawn cards contain exactly two Aces if it is known that they contain no Kings or Queens.

Is it 10C7 or 15C7? why? the reason I am confused is because, the card is not taken out, its still there, thats why i dont know which one to use

Solution

SEE THE TOTAL CASES WILL BE 15C7 AS IN THIS WAY ALL 7 CARDS CAN PE TAKEN OUT.

BUT AS PER THE QUESTION TWO ACES SHOULD BE THERE SO IT WILL BE 4C2 AND NO KINGS AND NO QUEENS THEREFORE THE REST 5 CARDS ARE TO BE FROM SIX OTHER CARDS

THEREFORE THE PROBABILITY WILL BE 4C2*6C5/15C7.