Question

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

Answer 1

Answer:

2598960 ways

Step-by-step explanation:

Given

Standard Deck = 52

Five-card hands

Required

Determine the number of ways

To solve this question, we make use of combination formula

$^nC_r = \frac{n!}{(n-r)!r!}$

Where n = 52 and r = 5

$^nC_r = \frac{n!}{(n-r)!r!}$ becomes

$^{52}C_5 = \frac{52!}{(52-5)!5!}$

$^{52}C_5 = \frac{52!}{47!5!}$

$^{52}C_5 = \frac{52 * 51 * 50 * 49 * 48 * 47!}{47! * 5 * 4 * 3 * 2 * 1}$

$^{52}C_5 = \frac{52 * 51 * 50 * 49 * 48}{5 * 4 * 3 * 2 * 1}$

$^{52}C_5 = \frac{311875200}{120}$

$^{52}C_5 = 2598960$

Hence, there are 2598960 ways