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.

Step-by-step 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

`(^7C_2)/(^9C_2)=(7!)/(2!*5!)*(2!*7!)/(9!)=(7*6*5!*7!)/(5!*9*8*7!)=(42)/(72)=0.5833`

Therefore, the probability is 0.5833