Question

A teacher selects 4 students from her class of 37 to work together on a project. How many ways are there for her to select the students? (b) A teacher selects students from her class of 37 students to do 4 different jobs in the classroom: pick up homework, hand out permission slips, staple worksheets, and organize the classroom library. Each job is performed by exactly one student in the class and no student can get more than one job. How many ways are there for her to select students and assign them to the jobs?

Answer 1

The correct answer is 66,045.

Explanation:

Number of students in the class is 37.

Total number of different kinds of jobs that is to be allotted to the students by their teacher is 4.

Therefore number of ways for the teacher to select a particular student for a particular job in which each job is done by exactly one student and no students gets more than one job is given by
`\left[\begin{array}{ccc}37\\4\end{array}\right]` =
`(37!)/(4! 33!)` = 66,045 ways.