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Question

Find the number 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?


Solution

Here total number of digits = 5

Number of digits used (no digit is repeated) = 4

Number of permutations = 5P4

=5!1!=5×4×3×2×1=120

Now the units place can be filled with any one of the digits 2, 4 for even number. 

Number of permutations

= 2P1=2!1!=2×1=2

Now the remaining three places can be filled with the remaining 4 digits.

Number of permutations = 4P3

4!1!=4×3×2×1=24

Hence total number of permutations of even number = 2×24=48.


Mathematics

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