# Five people are selected from 9 freshmen and 7 sophmores and seated in a row.

The probability a freshman is seated on each end and in the middle seat with sophmores in the other two seats is?
asked Dec 7, 2014

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 .

answered Dec 9, 2014