Question

52 Cards and you draw 5

- At least one is a 9 and four out of five of the cards belong to the same denomination (2,3,4,5,6,7,8,9,10,J,Q,K,A)

Answer 1

The number of ways to get 5 cards such that at least one is a 9 and four out of five of th cards belong to the same demonation is computed here as:

= Number of ways to select 5 cards such that there is a 9 and there are 4 other cards from same denomination + Number of ways to select all 9s and then fifth card from the remaining 48 cards

Therefore there are 96 ways to get the 5 card hand here.

The probability to get such a hand is computed here as:

= 96 / Total number of 5 card hands possible

Therefore 0.000037 is the required probability here.