Finite Math Examples

$\frac{5!}{0! (5!)} \cdot ({(0.3)}^{0} {(1 - 0.3)}^{5 - 0})$

Step 1

Simplify the numerator.

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Step 1.1

Expand $5!$ to $5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

$\frac{5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{0! (5!)} \cdot ({(0.3)}^{0} {(1 - 0.3)}^{5 - 0})$

Step 1.2

Multiply $5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

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Step 1.2.1

Multiply $5$ by $4$ .

$\frac{20 \cdot 3 \cdot 2 \cdot 1}{0! (5!)} \cdot ({(0.3)}^{0} {(1 - 0.3)}^{5 - 0})$

Step 1.2.2

Multiply $20$ by $3$ .

$\frac{60 \cdot 2 \cdot 1}{0! (5!)} \cdot ({(0.3)}^{0} {(1 - 0.3)}^{5 - 0})$

Step 1.2.3

Multiply $60$ by $2$ .

$\frac{120 \cdot 1}{0! (5!)} \cdot ({(0.3)}^{0} {(1 - 0.3)}^{5 - 0})$

Step 1.2.4

Multiply $120$ by $1$ .

$\frac{120}{0! (5!)} \cdot ({(0.3)}^{0} {(1 - 0.3)}^{5 - 0})$

Step 2

Simplify the denominator.

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Step 2.1

Expand $0!$ to $1$ .

$\frac{120}{15!} \cdot ({(0.3)}^{0} {(1 - 0.3)}^{5 - 0})$

Step 2.2

Expand $5!$ to $5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

$\frac{120}{1 (5 \cdot 4 \cdot 3 \cdot 2 \cdot 1)} \cdot ({(0.3)}^{0} {(1 - 0.3)}^{5 - 0})$

Step 2.3

Multiply $5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

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Step 2.3.1

Multiply $5$ by $4$ .

$\frac{120}{1 (20 \cdot 3 \cdot 2 \cdot 1)} \cdot ({(0.3)}^{0} {(1 - 0.3)}^{5 - 0})$

Step 2.3.2

Multiply $20$ by $3$ .

$\frac{120}{1 (60 \cdot 2 \cdot 1)} \cdot ({(0.3)}^{0} {(1 - 0.3)}^{5 - 0})$

Step 2.3.3

Multiply $60$ by $2$ .

$\frac{120}{1 (120 \cdot 1)} \cdot ({(0.3)}^{0} {(1 - 0.3)}^{5 - 0})$

Step 2.3.4

Multiply $120$ by $1$ .

$\frac{120}{1 \cdot 120} \cdot ({(0.3)}^{0} {(1 - 0.3)}^{5 - 0})$

Step 2.4

Multiply $120$ by $1$ .

$\frac{120}{120} \cdot ({(0.3)}^{0} {(1 - 0.3)}^{5 - 0})$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Cancel the common factor of $120$ .

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Step 3.1.1

Cancel the common factor.

$\frac{120}{120} \cdot ({(0.3)}^{0} {(1 - 0.3)}^{5 - 0})$

Step 3.1.2

Rewrite the expression.

$1 \cdot ({(0.3)}^{0} {(1 - 0.3)}^{5 - 0})$

Step 3.2

Simplify the expression.

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Step 3.2.1

Multiply ${(0.3)}^{0} {(1 - 0.3)}^{5 - 0}$ by $1$ .

${(0.3)}^{0} {(1 - 0.3)}^{5 - 0}$

Step 3.2.2

Anything raised to $0$ is $1$ .

$1 {(1 - 0.3)}^{5 - 0}$

Step 3.2.3

Multiply ${(1 - 0.3)}^{5 - 0}$ by $1$ .

${(1 - 0.3)}^{5 - 0}$

Step 3.2.4

Subtract $0.3$ from $1$ .

${0.7}^{5 - 0}$

Step 3.2.5

Subtract $0$ from $5$ .

${0.7}^{5}$

Step 3.2.6

Raise $0.7$ to the power of $5$ .

$0.16807$