Question

The number of selections of six persons including only one teacher from 4 teachers and 7 students is:

• A. 75
• B. 84
• C. 88
• D. 92

Hint:

When selecting a group from different categories, multiply the number of ways to select from each category to find the total number of selections.

Answer 1

The Correct Option is B

We need to select 6 persons including only 1 teacher from 4 teachers and 7 students. 
Step 1: First, select 1 teacher from 4 teachers. This can be done in: $$\binom{4}{1} = 4 \quad \text{ways}$$ 
Step 2: Next, select 5 students from 7 students. This can be done in: $$\binom{7}{5} = \binom{7}{2} = \frac{7 \times 6}{2 \times 1} = 21 \quad \text{ways}$$ 
Step 3: The total number of selections is: $$4 \times 21 = 84$$ Thus, the number of selections is 84.