Finite Math Examples

Find the Number of Possibilities 30 choose 3
C330
Step 1
Evaluate C330 using the formula Crn=n!(n-r)!r!.
30!(30-3)!3!
Step 2
Subtract 3 from 30.
30!(27)!3!
Step 3
Simplify 30!(27)!3!.
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Step 3.1
Rewrite 30! as 30292827!.
30292827!(27)!3!
Step 3.2
Cancel the common factor of 27!.
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Step 3.2.1
Cancel the common factor.
30292827!(27)!3!
Step 3.2.2
Rewrite the expression.
3029283!
3029283!
Step 3.3
Simplify the numerator.
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Step 3.3.1
Multiply 30 by 29.
870283!
Step 3.3.2
Multiply 870 by 28.
243603!
243603!
Step 3.4
Simplify the denominator.
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Step 3.4.1
Expand 3! to 321.
24360321
Step 3.4.2
Multiply 321.
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Step 3.4.2.1
Multiply 3 by 2.
2436061
Step 3.4.2.2
Multiply 6 by 1.
243606
243606
243606
Step 3.5
Divide 24360 by 6.
4060
4060
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 [x2  12  π  xdx ]