Question

Find the numbers of 4-digit numbers that can be formed using the digits 1, 2, 3, 4, 5, if no digit is repreated? How many of these will be even?

Answer 1

Out of 5 digits, 4-digit numbers are to be formed.

Such numbers are ${5_P}_4$ = $\frac{5!}{1!}=120$

When 2 is at unit's place, then remaining 3 places are filled in ${4_P}_3$ ways = 24 ways

When 4 ia at units place then 4 digit numbers are again = 24

Therefore,

Even 4 digit numbers = $2\times 24=48$