There are 2,598,960 possible 5-card hands that can be dealt from an ordinary 52-card deck. Of these, 5148 have all five cards of the same suit. (In poker such hands are called flushes.) The probability of being dealt such a hand (assuming randomness) is closest to
A) 1/4.
B) 1/100.
C) 1/500.
D) 1/1000.
E) 1/5148.

Question

Quizplus · Accepted Answer

The probability of being dealt a flush is the number of flush hands divided by the number of possible hands, which is: 
$$\frac{5148}{2598960} \approx 0.00198$$
This can also be written as $1/505.9$ which is closest to option C, 1/500.

There Are 2,598,960 Possible 5-Card Hands That Can Be Dealt