Question

If ²ⁿP₃ = 100 ⁿP₂, then the value of n is:
1. 1
2. 50
3. 13
4. 4

Answer 1

Correct Answer - Option 3 : 13

Concept:

Permutations and Combinations:

• P_r = \(\rm \frac{n!}{(n - r)!}\).
• n! = 1 × 2 × 3 × ... × n.
• 0! = 1.

 

Calculation:

Expanding the expression on both sides of the equation, we get:

2nP3 = 100 nP2

⇒ \(\rm \frac{2n!}{(2n - 3)!}=100\frac{n!}{(n - 2)!}\)

⇒ (2n)(2n - 1)(2n - 2) = 100(n)(n - 1)

⇒ 2n - 1 = 25, n ≠ 1.

⇒ n = 13.