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?

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Solution

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 = $2 \times 24 = 48$

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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 to these will be even?

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