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

Answer:

B) 2,598,960 hands

Step-by-step explanation:

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

$C(n,k)=nCk=\frac{n!}{k!(n-k)!}$

Where:

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

So:

$52C_5=\frac{52!}{5!(47!)}=2598960\hspace{3}hands$