Finite Math Examples

Find the Number of Possibilities 12 choose 5
C512
Step 1
Evaluate C512 using the formula Crn=n!(n-r)!r!.
12!(12-5)!5!
Step 2
Subtract 5 from 12.
12!(7)!5!
Step 3
Simplify 12!(7)!5!.
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Step 3.1
Rewrite 12! as 121110987!.
121110987!(7)!5!
Step 3.2
Cancel the common factor of 7!.
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Step 3.2.1
Cancel the common factor.
121110987!(7)!5!
Step 3.2.2
Rewrite the expression.
121110985!
121110985!
Step 3.3
Simplify the numerator.
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Step 3.3.1
Multiply 12 by 11.
13210985!
Step 3.3.2
Multiply 132 by 10.
1320985!
Step 3.3.3
Multiply 1320 by 9.
1188085!
Step 3.3.4
Multiply 11880 by 8.
950405!
950405!
Step 3.4
Simplify the denominator.
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Step 3.4.1
Expand 5! to 54321.
9504054321
Step 3.4.2
Multiply 54321.
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Step 3.4.2.1
Multiply 5 by 4.
9504020321
Step 3.4.2.2
Multiply 20 by 3.
950406021
Step 3.4.2.3
Multiply 60 by 2.
950401201
Step 3.4.2.4
Multiply 120 by 1.
95040120
95040120
95040120
Step 3.5
Divide 95040 by 120.
792
792
C512
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 [x2  12  π  xdx ]