Question

A team of 5 students is to be selected from 12 students. If two particular students are to be included in that team, then the number of ways that such team can be selected is:

• A. 792
• B. 180
• C. 120
• D. 90

Hint:

When certain members are already included in a selection, reduce the total pool of options and apply the combination formula.

Answer 1

The Correct Option is C

We are given that two particular students must be included in the team of 5. This means that we need to select 3 additional students from the remaining 10 students. The number of ways to select 3 students from 10 is given by the combination formula: \[ \binom{10}{3} = \frac{10 \times 9 \times 8}{3 \times 2 \times 1} = 120 \] Thus, the number of ways to form the team is \( 120 \), which is option (3).