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

First, 6 economists are selected for the triple rooms, yielding:
\(\binom{10}{6}\) ways.
Next, these 6 economists are divided into pairs for the 2 double rooms, which can be done in:
\(\frac{6!}{2^3 \cdot 3!}\) ways.
Consequently, the total number of ways is:
\(\binom{10}{6} \cdot \frac{6!}{2^3 \cdot 3!} = 210\)

Therefore, the correct answer is (a).