Question

1.How many ways are there to draw a five-card poker hand that contains five cards of the same suit?

2. How many ways are there to draw a five-card poker hand that contains at least one ace?

Answer 1

Question 1:

Number of suits = 4 ( spade, club, diamond, heart)

Number of cards in each suits = 13.

The possible cases to choose five cards.

All five cards are spades or All five cards are diamonds or all five cards are clubs or all five cards are hearts.

Hence total number of ways to choose five cards of the same suits is

Answer - 5148

Question 2:

Numbers of aces in a pack = 4

Number of remaining cards = 48

Possible cases are

i) One ace and 4 remaining cards.

ii) two aces and 3 remaining cards.

iii) three aces and 2 remaining cards .

iv) 4 aces and 1 remaining card.

Hence number of ways to choose 5 cards contains at least 1 ace is

=886656

Answer - 886656.