Question

The director of a film festival received 9 submissions, 7 of which were romantic comedies.If the director randomly chose to play 6 of the submissions on the first day of the festival, what is the probability that all of them are romantic comedies?Write your answer as a decimal rounded to four decimal places.

Answer 1

Given:

it is given that the director of a film festival received 9 submissions, 7 of which were romantic comedies. the director randomly chose to play 6 of the submissions on the first day .

Find:

we have to find the probability that all the six submission chosed by director are romantic comedies.

Explanation:

The director can chose the 6 submissions out of 9 in

$^9C_6$

ways.

and all the 6 submission can be out of 7 comedies submission by

$^7C_6$

ways.

Therefore, the probability that all the six are romantic comedies is given by

$\frac{^7C_2}{^9C_2}=\frac{7!}{2!\times5!}\times\frac{2!\times7!}{9!}=\frac{7\times6\times5!\times7!}{5!\times9\times8\times7!}=\frac{42}{72}=0.5833$

Therefore, the probability is 0.5833