Question

In how many ways can 10 economists attending a conference be accommodated in 2 triple sharing and 2 double sharing hotel rooms?

• A. 210
• B. 420
• C. 630
• D. 1260

Hint:

For combinatorics problems involving selections and partitions, break the task into smaller steps and use factorials and combinations.

Answer 1

The Correct Option is A

We need to choose 6 economists to stay in the triple rooms, which can be done in:
\(\binom{10}{6}\) ways. 
After selecting 6 economists, we divide them into pairs for the 2 double rooms. The number of ways to divide 6 economists into pairs is:
\(\frac{6!}{2^3 \cdot 3!}\)
Hence, the total number of ways is:
\(\binom{10}{6} \cdot \frac{6!}{2^3 \cdot 3!} = 210\)

Thus, the correct answer is (a).