Q. 314.3( 7 Votes )

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

Answer :

Given, digits which can be used to make numbers are 1, 2, 3, 4 and 5


The number of these digits are 5


To find: total number of 4-digit numbers with no digit repeated


Formula used:


Number of arrangements of n things taken r at a time = P(n, r)



The total number of ways


= the number of arrangements of 5 things taken 4 at a time


= P(5, 4)





= 120


Hence, total number of 4-digit numbers using digits 1 to 5 with no digit repeated are 120


Now, for 4-digit even number from digits 1, 2, 3, 4 and 5:


Let 4-digit even number be



Fix the position of unit’s place i.e. t as an even number for which we have 2 choices (2 or 4)


Now, for position x we have remaining 4 choices


Similarly, for position y and z we have 3 and 2 choices respectively


Total number of even numbers are


= multiplication of choices of x y z t


= 4 × 3 × 2 × 2


= 48


Hence, total number of 4-digit numbers using digits 1 to 5 with no digit repeated are 48


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