Question

find the probability of being delt 5 clubs and 3 cards with one of each remaining suit in 8 card poker

Answer 1

Answer: 0.003757(approx).

Explanation:

Total number of combinations of selecting r things out of n things is given by:-

`^nC_r=(n!)/(r!(n-r)!)`

Total cards in a deck = 52

Total number of ways of choosing 8 cards out of 52 =
`^(52)C_8`

Total number of ways to choose 5 clubs and 3 cards with one of each remaining suit =
`^(13)C_5*^(13)C_1*^(13)C_1*^(13)C_1` [since 1 suit has 13 cards]

The required probability =
`=(^(13)C_5*^(13)C_1*^(13)C_1*^(13)C_1)/(^(52)C_8)`

`=((13!)/(5!8!)*13*13*13)/((52!)/(8!44!))\\\\=(24167)/(6431950)\\\\\approx0.003757`

Hence, the required probability is 0.003757 (approx).