Question

\(\frac{100}{10!} = \frac{1}{8!} + \frac{x}{9!}\). Find x.

(a) 1

(b) 2

(c) 3

(d) 4

This question was addressed to me by my school teacher while I was bunking the class.

The origin of the question is Permutations-1 topic in section Permutations and Combinations of Mathematics – Class 11

Answer 1

Correct option is (a) 1

Easiest explanation: \(\frac{100}{10!} = \frac{1}{8!} + \frac{x}{9!}\).

We know, n! = n.(n-1). (n-2). (n-3) …………… = n(n-1)!

\(\frac{100}{10.9.8!} = \frac{1}{8!} + \frac{x}{9.8!}\)

=> \(\frac{100}{10.9} = \frac{1}{1} + \frac{x}{9}\)

=> \(\frac{10}{9} = 1 + \frac{x}{9}\)

=> \(\frac{x}{9} = \frac{10}{9} – 1 = \frac{1}{9}\)

=> x=1.