Respuesta :
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 [tex]^{5} \mathrm{C}_{4} \text { Ways. }[/tex]
[tex]\mathrm{n} \mathrm{C}_{\mathrm{r}}=\frac{n !}{(n-r) ! r !}[/tex]
[tex]5 \mathrm{C}_{4}=\frac{5 !}{(5-4) ! 4 !}=\frac{5 \times 4 !}{1 ! 4 !}=5[/tex]
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
[tex]5 \times 4 !=5 !=5 \times 4 \times 3 \times 2 \times 1=120 \text { ways }[/tex]
Hence, we can form 120 different numbers.
