Question

A standard deck of 52 playing cards has 4 suits with 13 different cards in each suit. How many different five-card hands are possible?

A) 260 hands
B) 2,598,960 hands
C) 24,380 hands
D) 311,875,200 hands

Answer 1

I think the answer is B

Answer 2

B) 2,598,960 hands

Explanation:

This is a combination problem. So we can use the next formula:

`C(n,k)=nCk=(n!)/(k!(n-k)!)`

Where:

`n=Number\hspace{3}of\hspace{3}elements=52\\k=Number\hspace{3}of\hspace{3}combinations= 5`

So:

`52C_5=(52!)/(5!(47!))=2598960\hspace{3}hands`