The number of six digit even numbers that can be formed, using the digits 1,2,3,4,5,6 and 7 , so that digits do not repeat, is-

Question

The number of six digit even numbers that can be formed, using the digits 1,2,3,4,5,6 and 7 , so that digits do not repeat, is- (A) 720 (B) 288 (C) 144 (D) 2160

Tardigrade Admin · Accepted Answer

Unit place can be filled up with any one of 2,4,6 in 3 ways. The remaining place can be filled up ( 6 C 5 .5. !) ways. ⇒ Required number is ( 6 C5 ⋅ 5 !) ⋅ 3 !=2160

Q. The number of six digit even numbers that can be formed, using the digits $1, 2, 3, 4, 5, 6$ and $7$ , so that digits do not repeat, is-

$720$

$288$

$144$

$2160$

Unit place can be filled up with any one of $2, 4, 6$ in 3 ways. The remaining place can be filled up $(^{6} C_{5} .5$ !) ways.
$\Rightarrow$ Required number is $(^{6} C_{5} \cdot 5!) \cdot 3! = 2160$

Q. The number of six digit even numbers that can be formed, using the digits 1,2,3,4,5,6 and 7 , so that digits do not repeat, is-

720

288

144

2160