How many hands of 5-draw poker contain the ace of hearts? What is the probability that a 5-card draw hand contains the ace of hearts?

Probability that a 5-card draw hand contains the ace of hearts = 0.0962

Explanation:

A deck of Cards = 52 random card = 5 To find the number of 5 - stud poker hands there?

a) The selection of 5cards from a deck of 52cards = The knowledge of combination comes in

= nCr = n! / (n-r) ! r!

= 52C5 = 52! / (52-5) !5!

= 2598960, hence there are 2598960 ways of selecting 5cards from a deck of 52cards

b) There are 1 ace of heart in a deck of cards, therefore, the number of ways of choosing 1 ace of heart and 4 other cards = nCr

= 1C1 X 51C4

= 1 X 51! / (51-4) !4!

= 249900

c) To find the probability that the 5 cards drawn contain an ace of hearts

= P (5 cards drawn contain an ace of hearts) = number of favorable outcomes / total number of outcomes

= 249900 / 2598960

= 0.0962