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,
[tex]=\ ^{52}\text{C}_6=20358520[/tex]
In a deck of 52 cards, 13 cards are of spades. So drawing 2 spades out of 13 is,
[tex]=\ ^{13}\text{C}_2=78[/tex]
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,
[tex]=\ ^{39}\text{C}_4=82251[/tex]
The probability of getting exactly 2 of the cards are spades out of 6 cards will be,
[tex]=\dfrac{\ ^{13}\text{C}_2\times ^{39}\text{C}_4}{\ ^{52}\text{C}_6}=\dfrac{78\times 82251}{20358520}=0.315[/tex]
