Question

Four students have to be chosen: 2 girls as the captain and vice-captain and 2 boys as the captain and vice-captain of the school. There are 15 eligible girls and 12 eligible boys. In how many ways can they be chosen if Sunita is sure to be the captain?

• A. 114
• B. 1020
• C. 360
• D. 1848
• E. 1500

Hint:

Jab posts distinct hon (captain vs vice-captain), tab permutations use karo: \({}^{n}P_{r} = n \times (n-1) \times \cdots\). Agar sirf selection hoti (without roles), tab combinations \(\binom{n}{r}\) use hota.

Answer 1

The Correct Option is D

Step 1: Fix Sunita as the Girls' Captain.
Sunita's position (Girls' Captain) is fixed, so there is \(1\) way for this role.

Step 2: Choose the Girls' Vice-Captain.
Remaining eligible girls \(= 15 - 1 = 14\).
Hence, Girls' Vice-Captain can be chosen in \(14\) ways.

Step 3: Assign Boys' Captain and Boys' Vice-Captain (distinct roles).
Number of ways to assign two distinct posts to boys \(= {}^{12}P_{2} = 12 \times 11 = 132\).

Step 4: Apply the Multiplication Principle.
Total ways \(= 1 \times 14 \times 132 = 1848\).

Final Answer:
\[ \boxed{1848} \]