Question

In how many ways can 4 boys be seated on 10 different chairs in a row?

• A. 720
• B. 1080
• C. 3080
• D. 5040

Hint:

Seating problems with distinct chairs always require choosing the chairs first and then permuting the people.

Answer 1

The Correct Option is D

Step 1: Select 4 chairs out of 10.
Number of ways = \( \binom{10}{4} \).
Step 2: Arrange 4 boys in those 4 selected chairs.
Arrangements = \( 4! \).
Step 3: Multiply selections and arrangements.
\( \binom{10}{4} \times 4! = \frac{10!}{6!4!} \times 24 = 210 \times 24 = 5040.\)
Step 4: Conclusion.
Thus the total number of ways is 5040.