Question

If 6 cards are drawn at random from a standard deck of 52 cards, what is the probability that exactly 2 of the cards are spades?

Answer 1

Answer:

The probability of getting exactly 2 of the cards are spades out of 6 cards will be 0.315

Step-by-step explanation:

6 cards are drawn at random from a standard deck of 52 cards.

The number ways 6 cards can be drawn from a deck of 52 cards will be,

$=\ ^{52}\text{C}_6=20358520$

In a deck of 52 cards, 13 cards are of spades. So drawing 2 spades out of 13 is,

$=\ ^{13}\text{C}_2=78$

As exactly 2 must be spades, so the remaining 4 cards must be drawn from other 39 cards of other suits. This can be done in,

$=\ ^{39}\text{C}_4=82251$

The probability of getting exactly 2 of the cards are spades out of 6 cards will be,

$=\dfrac{\ ^{13}\text{C}_2\times ^{39}\text{C}_4}{\ ^{52}\text{C}_6}=\dfrac{78\times 82251}{20358520}=0.315$