Question

How many different five-card hands can be dealt from a standard deck of fifty-two cards?

Answer 1

2598960 ways

Explanation:

Given

Standard Deck = 52

Five-card hands

Required

Determine the number of ways

To solve this question, we make use of combination formula

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

Where n = 52 and r = 5

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

`^(52)C_5 = (52!)/((52-5)!5!)`

`^(52)C_5 = (52!)/(47!5!)`

`^(52)C_5 = (52 * 51 * 50 * 49 * 48 * 47!)/(47! * 5 * 4 * 3 * 2 * 1)`

`^(52)C_5 = (52 * 51 * 50 * 49 * 48)/(5 * 4 * 3 * 2 * 1)`

`^(52)C_5 = (311875200)/(120)`

`^(52)C_5 = 2598960`

Hence, there are 2598960 ways