Question

Permutation/Combination Derek shuffled a pack of 52 playing cards and asked his friends, Ian to choose any 5 cards. How many different 5 cars hands are possible?

Answer 1

Given the question in the question tab, the following are the solution steps to get possible 5 card hands

Step 1: Identify the type of problem in the question

Ian is choosing a subset of size 5 from a set of size 52. Note that the order in which he is dealt these 5 cards is irrelevant. Thus, order doesn’t matter. Thus, this is a combination problem.

Step 2: Write the formula for finding combination

`\text{nCr}=(n!)/((n-r)!r!)`

Step 3: Find the possible different 5 card hands

`\begin{gathered} n=52,r=5 \\ \text{nCr}=(n!)/((n-r)!r!) \\ 52\text{C5}=(52!)/((52-5)!5!)=(52!)/(47!5!) \\ =(52*51*50*49*48*47!)/(47!*5!) \\ =(52*51*50*49*48)/(5!)=2598960 \end{gathered}`

Hence, there are 2598960 different possible card hands.