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?

a) 16 ways

b) 188 ways

c) 39 ways

d) 51 ways

Step-by-step 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