How many different four-digit even positive integers can be made using the digits 1, 2, 3, 4, 5 if no digit can be used more than once?

120 different four-digit even positive integers can be made using the digits 1, 2, 3, 4, 5 if no digit can be used more than once

Solution:

Given, digits are 1, 2, 3, 4, 5

We have to find the number of ways in which 4 digit number can be made form the given digits with out repetition.

Now, first we have to select 4 digits out of 5 digits to form a number.

As it is just combination, we can take in

So, we can select 4 digits in 5 ways.

And now, we can arrange them in 4! Factorial ways.

Then, total 5 x 4! Ways are available  

Hence, we can form 120 different numbers.

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