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  4. Number of seven digit numbers, which can be formed with non-zero distinct digits such that it starts and end with a prime digit and middle digit is an even digit, is-

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Q. Number of seven digit numbers, which can be formed with non-zero distinct digits such that it starts and end with a prime digit and middle digit is an even digit, is-

Permutations and Combinations

Solution:

Csae-I: If middle digit is $2$
then numbers $3.2 .6 .5 .4 .3=2160$
Case-II: If middle digit is not $2$
then number of $4.3 .3 .6 .5 .4 .3 .=12960$
So total number of 7 -digit numbers
$2160+12960=15120$