Question

Four new students have to be assigned a tutor. there are seven possible tutors and none of them will accept more than one student. in how many ways can the tutor assignment be done?

Answer 1

There are 35 different ways to assign four new students to seven possible tutors, given that each tutor will accept only one student.

Step-by-step explanation:

The student has asked a question related to combinatorics, specifically about tutor assignment. We have four new students and seven possible tutors, with the condition that each tutor can accept only one student. To calculate the number of ways the assignment can be done, we use combinations. Since the order of assignments doesn't matter, we need to select 4 tutors out of the 7 without considering the order. The formula for combinations is given by:

C(n, k) = n! / (k!(n - k)!), where 'n' is the total number of items, 'k' is the number of items to be chosen, and '!' denotes factorial.

In this case, n=7 and k=4, therefore:

C(7, 4) = 7! / (4!(7 - 4)!) = (7*6*5*4!) / (4!*3*2*1) = 35

Therefore, 35 different ways exist for the assignment of the four new students to tutors.

Answer 2

28 tutoring assignments can be done