how many 4- digit can be formed?

Question

Using the digits 1, 2, 3 and 5, how many 4-digit numbers can be formed if :

the first digit must be 1 and repetition of the digits is allowed?

the first digit must be 1 and repetition of the digits is not allowed?

the number must be divisible by 2 and repetition is allowed?

the number must be divisible by 2 and repetition is not allowed?

Answer 1

For the first digit forced to 1 and repetition allowed,

write 1×4×4×4 or 64.

For the first digit forced to 1 and repetition banned,

write 1×3×2×1 or 6.

A mandatory even number forces the last digit to 2.

With repetition allowed, write 4×4×4×1 or 64.

A mandatory even number forces the last digit to 2.

With repetition banned, write 3×2×1×1 or 6.