Question

1. If ⁿC₂ = ⁿC₈ then find n

2. Find n if ⁿP₅ = 42 × ⁿP₃; n> 4

Answer 1

1. n = 2 + 8 = 10.

2. DAUGHTER this word has 8 different letters. A, U, E are the vowels. Treat these 3 as one unit, then there are 6 units and can be permuted in 6! ways. The above vowels can be permuted in 3! ways. Hence the total number of words is 6! × 3! = 4320.