यदि nC9 = nC8 है तो nC17 खोजें?

Question

Question

This question was previously asked in

AAI ATC Junior Executive 25 March 2021 Official Paper (Shift 2)

Answer 1

दिया गया है:

nC9 = nC8

प्रयुक्त सूत्र:

nCr = \(\frac{n!}{r!(n - r)!}\)

गणना:

हमारे पास है,

nC9 = nC8

⇒ \(\frac{n!}{9!(n - 9)!} = \frac{n!}{8!(n - 8)!}\)

⇒ \(\frac{n!(n - 8)!}{n!(n - 9)!} = \frac{9!}{8!}\)

⇒ \(\frac{(n - 8)!}{(n - 9)!} = \frac{9!}{8!}\)

⇒ \(\frac{(n - 8)(n - 9)!}{(n - 9)!} = \frac{9 \times 8!}{8!}\)

⇒ n - 8 = 9

⇒ n = 17

अब हमें nC17 ज्ञात करना है

n = 17 लेने पर

⇒ 17C17

⇒ \(\frac{17!}{17!(17 - 17)!}\)

⇒ \(\frac{17!}{17! \times 0!}\)

⇒ \(\frac{17!}{17! \times 1}\)

⇒ 1

∴ nC17 का मान 1 है।