Question

45. If \( { }^{7} P_{n} \div{ }^{7} P_{n-3}=60 \) the value of \( n \) is (a) 8 (b) 4 (c) 5 (d) 2

Answer 1

\(^7P_n \div\,^7P_{n-3} = 60\)

⇒ \(\frac{7!}{(7 -n)!}\div \frac{7!}{(7 - (n-3))!} = 60\)

⇒ \(\frac{(10- n)!}{(7 - n)! }=60\)

⇒ \(\frac{(10 - n)(9 -n)(8 -n)(7 -n)!}{(7 - n)!}= 60\)

⇒ (10 - n) (9 - n) (8 - n) = 5 x 4 x 3

⇒ (10 - n) (9 - n) (8 - n) = (10 - 5) (9 - 5) (8 - 5)

∴ n = 5