Question

The number of all three element subsets of the set \(\{a_1,a_2,a_3,\ldots,a_n\}\) which contain \(a_3\) is:

• A. \({}^nC_3\)
• B. \({}^{n-1}C_3\)
• C. \({}^{n-1}C_2\)
• D. None of these

Hint:

Fix required elements first, then choose remaining elements.

Answer 1

The Correct Option is C

Step 1: Fix \(a_3\) in the subset.
Step 2: Choose remaining 2 elements from the other \(n-1\) elements. \[ \text{Number of subsets}={}^{n-1}C_2 \]