To evaluate [tex]\(5! + 2!\)[/tex], let's break it down into clear steps:
1. Find the factorial of 5 ([tex]\(5!\)[/tex]):
The factorial of a number [tex]\(n!\)[/tex] is the product of all positive integers less than or equal to [tex]\(n\)[/tex].
[tex]\[
5! = 5 \times 4 \times 3 \times 2 \times 1
\][/tex]
Calculating this step-by-step:
[tex]\[
5 \times 4 = 20
\][/tex]
[tex]\[
20 \times 3 = 60
\][/tex]
[tex]\[
60 \times 2 = 120
\][/tex]
[tex]\[
120 \times 1 = 120
\][/tex]
So, [tex]\(5! = 120\)[/tex].
2. Find the factorial of 2 ([tex]\(2!\)[/tex]):
[tex]\[
2! = 2 \times 1
\][/tex]
Calculating this:
[tex]\[
2 \times 1 = 2
\][/tex]
So, [tex]\(2! = 2\)[/tex].
3. Add the two factorials [tex]\(5! + 2!\)[/tex]:
[tex]\[
5! + 2! = 120 + 2
\][/tex]
Adding these together:
[tex]\[
120 + 2 = 122
\][/tex]
Therefore, the answer to [tex]\(5! + 2!\)[/tex] is [tex]\(122\)[/tex].
