Question

Taking two cards, one by one, from a standard 52-card deck, how many different ways are there if (a). the first card is an ace and the second card is a king? (b). the first card is an ace and the second card is not a king? (c). the first card is a heart and the second card is an ace? (d). there is at least one ace in the two cards?

Answer 1

a) 16 ways

b) 188 ways

c) 39 ways

d) 51 ways

Explanation:

A standard deck of 52 cards consists of 4 suits of spades, hearts, diamonds and clubs. Each suit contains 13 cards. According to this:

a)

First card is an ace = 4 possible cards

Second card is a king = 4 possible cards

4 X 4 = 16 ways

b)

First card is an ace = 4 possible cards

Second card is not a king= 51 cards - 4 kings = 47 possible cards

4 X 47 = 188 ways

c)

First card is a heart = 13 possible cards

Second card is an ace = 4 aces - 1 heart ace = 3 possible cards

13 X 3 = 39 ways

d)

First card an ace = 1 card

second card, any other card = 51 possible cards

1 X 51 = 51 ways