Five people are selected from 9 freshman and 7 sophomores and seated in a row.

Question

The probability a freshman is seated on each end and in the middle seat with sophomores in the other two seats is

a. 14/429

b. 5/16

c. 21/520

d. 5/32

Answer 1

 

Total number of people = 9 freshmen + 7 sophomores = 16 .

There are 16 people in a group .

Selecting five people in the following way in a row .

Fresher

Sophomores

Fresher

Sophomores

Fresher

The probability of fresher seated in first place = (Number of freshmen) / (total Number of people ) = 9/16 .

The probability of fresher seated in middle place = (Number of freshmen remains) / (total Number of people remain ) = 8/15 .

The probability of fresher seated in end of the row  = (Number of freshmen remains) / (total Number of people remain ) = 7/14 .

The probability of sophomores seated in 2nd place = (Number of sophomores) / (total Number of people remain ) = 7/13 .

The probability of sophomores seated in 4th place = (Number of sophomores remains ) / (total Number of people remain ) = 6/12 .

 

The probability a freshman is seated on each end and in the middle seat with sophomores in the other two seats is 

                        

Therefore the required probability is 21/520 .

Option (c) is the correct answer.