Question

In how many ways can a team of 4 students be chosen from a class of 8 students if one particular student is already considered ineligible and another particular student already pre-qualified?

a) 70
b) 56
c) 35
d) 28

Answer 1

A team of 4 students is to be selected from a pool of 8, excluding one ineligible student and including one pre-qualified student. The task is to choose 3 more students from the remaining 6, which can be done in 20 different ways according to the combinations formula.

Step-by-step explanation:

The question asks in how many ways a team of 4 students can be chosen from a class of 8 students given that one student is ineligible and another is already pre-qualified. We begin with 8 students. One student is ineligible, reducing the pool to 7 students. One student is pre-qualified, so we need to choose the remaining 3 team members from the remaining 6 students.

To calculate the number of combinations, we use the combinations formula which is C(n, k) = n! / (k!(n - k)!), where n is the total number of items, and k is the number of items to choose.

Here, C(6, 3) = 6! / (3!(6 - 3)!) = 20, so there are 20 different ways to choose the remaining 3 team members from 6 students.