There are 11 students on the tennis team. The coach selects 3 of them to go to a tennis clinic. In how many ways can he choose 3 of the 11 students?A.990B.165C.330D.55SUBMITarrow_backPREVIOUS

The problem is asking for the number of combinations of 11 students taken 3 at a time. This is a combination problem because the order in which the students are selected does not matter.

The formula for combinations is:

C(n, k) = n! / [k!(n-k)!]

where:

• n is the total number of options,
• k is the number of options chosen at a time,
• "!" denotes factorial, which means multiplying all positive integers up to that number.

So, in this case, n = 11 (the total number of students) and k = 3 (the number of students the coach is selecting).

Substituting these values into the formula gives:

C(11, 3) = 11! / [3!(11-3)!]

Calculating the factorials:

11! = 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 3! = 3 × 2 × 1 (11-3)! = 8! = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

Substituting these values back into the formula gives:

C(11, 3) = (11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) / [(3 × 2 × 1) × (8 × 7 × 6 × 5 × 4 × 3 × 2 × 1)]

Simplifying this expression gives:

C(11, 3) = (11 × 10 × 9) / (3 × 2 × 1) = 165

So, the coach can choose 3 of the 11 students in 165 different ways. Therefore, the answer is B. 165.