Question

The number of four digit numbers that can be formed from the digits 2,3,5,6,7,8 so that the digits do not repeat and the terminal digits are even is

• A. 42
• B. 78
• C. 72
• D. 36
• E. None of these

Answer 1

The correct option is C 72

If the first digit and last digit of the four digit number needs to be even, then we have to choose numbers out of 2, 6 and 8

The first digit can be chosen in 3 ways and the last digit in 2 ways = 3$\times$2=6 ways

The remaining two digits can be chosen and arranged among the remaining 4 digits in ${}^4$P${}_2$ ways = 12 ways

Total number of ways = 6$\times$12=72 ways