Finite Math Examples

Find the Number of Possibilities 100 choose 18
Step 1
Evaluate using the formula .
Step 2
Subtract from .
Step 3
Simplify .
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Step 3.1
Rewrite as .
Step 3.2
Cancel the common factor of .
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Step 3.2.1
Cancel the common factor.
Step 3.2.2
Rewrite the expression.
Step 3.3
Simplify the numerator.
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Step 3.3.1
Multiply by .
Step 3.3.2
Multiply by .
Step 3.3.3
Multiply by .
Step 3.3.4
Multiply by .
Step 3.3.5
Multiply by .
Step 3.3.6
Multiply by .
Step 3.3.7
Multiply by .
Step 3.3.8
Multiply by .
Step 3.3.9
Multiply by .
Step 3.3.10
Multiply by .
Step 3.3.11
Multiply by .
Step 3.3.12
Multiply by .
Step 3.3.13
Multiply by .
Step 3.3.14
Multiply by .
Step 3.3.15
Multiply by .
Step 3.3.16
Multiply by .
Step 3.4
Simplify the denominator.
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Step 3.4.1
Expand to .
Step 3.4.2
Multiply .
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Step 3.4.2.1
Multiply by .
Step 3.4.2.2
Multiply by .
Step 3.4.2.3
Multiply by .
Step 3.4.2.4
Multiply by .
Step 3.4.2.5
Multiply by .
Step 3.4.2.6
Multiply by .
Step 3.4.2.7
Multiply by .
Step 3.4.2.8
Multiply by .
Step 3.4.2.9
Multiply by .
Step 3.4.2.10
Multiply by .
Step 3.4.2.11
Multiply by .
Step 3.4.2.12
Multiply by .
Step 3.4.2.13
Multiply by .
Step 3.4.2.14
Multiply by .
Step 3.4.2.15
Multiply by .
Step 3.4.2.16
Multiply by .
Step 3.4.2.17
Multiply by .
Step 3.5
Cancel the common factor of and .
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Step 3.5.1
Factor out of .
Step 3.5.2
Cancel the common factors.
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Step 3.5.2.1
Factor out of .
Step 3.5.2.2
Cancel the common factor.
Step 3.5.2.3
Rewrite the expression.
Step 3.6
Cancel the common factor of and .
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Step 3.6.1
Factor out of .
Step 3.6.2
Cancel the common factors.
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Step 3.6.2.1
Factor out of .
Step 3.6.2.2
Cancel the common factor.
Step 3.6.2.3
Rewrite the expression.
Step 3.6.2.4
Divide by .
Step 3.7
Multiply by .