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?

Question

asked Sep 17, 2020 181k views

1 Answer

Suhas Gavad · Answer 1 · 2020-09-22T06:15:46+0000

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
$^(5) \mathrm{C}_(4) \text { Ways. }$

$\mathrm{n} \mathrm{C}_{\mathrm{r}}=(n !)/((n-r) ! r !)$

$5 \mathrm{C}_(4)=(5 !)/((5-4) ! 4 !)=(5 * 4 !)/(1 ! 4 !)=5$

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

$5 * 4 !=5 !=5 * 4 * 3 * 2 * 1=120 \text { ways }$

Hence, we can form 120 different numbers.