18 ! is not divisible by

Question

18 ! is not divisible by (A) (2 !)9 (B) (9 !)2 (C) (6 !)2 (D) None of these

Tardigrade Admin · Accepted Answer

18 ! has 9 groups of 2 consecutive integers ⇒ 18 ! is divisible by (2 !)9 18 ! has 2 groups of 9 consecutive integers ⇒ 18 ! is divisible by (9 !)2 18 ! has 3 groups of 6 consecutive integers ⇒ 18 ! is divisible by (6 !)3, hence divisible by (6 !)2

Q. $18!$ is not divisible by

$(2!)^{9}$

$(9!)^{2}$

$(6!)^{2}$

None of these

Q. 18! is not divisible by

(2!)9

(9!)2

(6!)2

None of these

18! has 9 groups of 2 consecutive integers ⇒18! is divisible by (2!)9 18! has 2 groups of 9 consecutive integers ⇒18! is divisible by (9!)2 18! has 3 groups of 6 consecutive integers ⇒18! is divisible by (6!)3, hence divisible by (6!)2

Q. $18!$ is not divisible by

$(2!)^{9}$

$(9!)^{2}$

$(6!)^{2}$