Question

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

• A. $144$
• B. $72$
• C. $288$
• D. $720$

Answer 1

The correct option is D $720$

Terminal digits are the first and last digits. Since, terminal digits are even.

$\therefore$ 1st place can be filled in 3 ways and last place can be filled in 2 ways and remaining places can be filled in ${}^5{P}_4=120$ ways

Hence, the number of six digit number, so that the terminal digits are even, is $3\times 120\times 2=720$.

Hence, option D is correct.