Cards are drawn one by one without replacement from a pack of 52 cards. The probability that 10 cards will precede the first ace is

Let event A be drawing 9 cards which are not ace and B be drawing an ace card. Therefore, the required probability is P(A∩B)=P(A)×P(B)Now, there are four aces and 48 other cards. Hence,P(A)= 48C9 52C9After having drawn 9 non-ace cards, the 10th card must be ace. Hence,P(B)= 4C1 42C1=442Hence,P(A∩B)= 48C9 52C9442