Question

An experiment consists of dealing 7 cards from a standard deck of 52 playing cards. What is the probability of being dealt exactly 4 clubs and 3 spades?

Answer 1

Answer: 0.00153

Step-by-step explanation:

Given: An experiment consists of dealing 7 cards from a standard deck of 52 playing cards.

Number of ways of dealing 7 cards from 52 cards = $^{52}C_7$

Since there are 13 clubs and 13 spades.

Number of ways of getting exactly 4 clubs and 3 spades=$^{13}C_4\times\ ^{13}C_3$

Now, the probability of being dealt exactly 4 clubs and 3 spades

$=\dfrac{^{13}C_4\times\ ^{13}C_3}{^{52}C_7}\\\\\\=\dfrac{{\dfrac{13!}{4!(9!)}\times\dfrac{13!}{3!10!}}}{\dfrac{52!}{7!45!}}\\\\=\dfrac{715\times286}{133784560}\\\\=0.00152850224271\approx0.00153$

Hence,  the probability of being dealt exactly 4 clubs and 3 spades = 0.00153