Finite Math Examples

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

Step 1

Simplify the numerator.

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Step 1.1

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

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

Step 1.2

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

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Step 1.2.1

Multiply $5$ by $4$ .

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

Step 1.2.2

Multiply $20$ by $3$ .

$\frac{60 \cdot 2 \cdot 1}{2! (3!)} \cdot ({(0.3)}^{2} {(1 - 0.3)}^{5 - 2})$

Step 1.2.3

Multiply $60$ by $2$ .

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

Step 1.2.4

Multiply $120$ by $1$ .

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

Step 2

Simplify the denominator.

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Step 2.1

Expand $2!$ to $2 \cdot 1$ .

$\frac{120}{2 \cdot 13!} \cdot ({(0.3)}^{2} {(1 - 0.3)}^{5 - 2})$

Step 2.2

Multiply $2$ by $1$ .

$\frac{120}{23!} \cdot ({(0.3)}^{2} {(1 - 0.3)}^{5 - 2})$

Step 2.3

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

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

Step 2.4

Multiply $3 \cdot 2 \cdot 1$ .

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Step 2.4.1

Multiply $3$ by $2$ .

$\frac{120}{2 (6 \cdot 1)} \cdot ({(0.3)}^{2} {(1 - 0.3)}^{5 - 2})$

Step 2.4.2

Multiply $6$ by $1$ .

$\frac{120}{2 \cdot 6} \cdot ({(0.3)}^{2} {(1 - 0.3)}^{5 - 2})$

Step 3

Simplify the expression.

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Step 3.1

Multiply $2$ by $6$ .

$\frac{120}{12} \cdot ({(0.3)}^{2} {(1 - 0.3)}^{5 - 2})$

Step 3.2

Divide $120$ by $12$ .

$10 \cdot ({(0.3)}^{2} {(1 - 0.3)}^{5 - 2})$

Step 3.3

Raise $0.3$ to the power of $2$ .

$10 \cdot (0.09 {(1 - 0.3)}^{5 - 2})$

Step 3.4

Subtract $0.3$ from $1$ .

$10 \cdot (0.09 \cdot {0.7}^{5 - 2})$

Step 3.5

Subtract $2$ from $5$ .

$10 \cdot (0.09 \cdot {0.7}^{3})$

Step 3.6

Raise $0.7$ to the power of $3$ .

$10 \cdot (0.09 \cdot 0.343)$

Step 4

Multiply $10 (0.09 \cdot 0.343)$ .

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Step 4.1

Multiply $0.09$ by $0.343$ .

$10 \cdot 0.03087$

Step 4.2

Multiply $10$ by $0.03087$ .

$0.3087$