Consider selecting one card at a time from a 52card deck Not

Consider selecting one card at a time from a 52-card deck. (Note: There are 4 aces in a deck of cards)

a. If the card selection is without replacement, what is the probability that the first card is an ace and the second card is also an ace? (Express the answer in simplest fraction form)

Solution

Drawing a 2 card from the deck = 52 C 2
Drawing an Ace card, we have 4 Ace card in a pack of 52, First card drawn is Ace = 4 C 1 and the Second drawn Ace card it is 3 C 1.
probability that the first card is an ace and the second card is also an ace = 4 C 1 * 3 C 1 / 52 C 2 = (4 * 3 ) (2 * 1) / (52 * 51) = 24 / 2652= 2/221 = 0.00904977