Finite Math Examples

$(\frac{16!}{1! (16 - 1!)}) (0.23) \cdot {(0.77)}^{15}$

Step 1

Simplify the numerator.

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Step 1.1

Expand $16!$ to $16 \cdot 15 \cdot 14 \cdot 13 \cdot 12 \cdot 11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

$\frac{16 \cdot 15 \cdot 14 \cdot 13 \cdot 12 \cdot 11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{1! (16 - 1!)} \cdot 0.23 \cdot {(0.77)}^{15}$

Step 1.2

Multiply $16 \cdot 15 \cdot 14 \cdot 13 \cdot 12 \cdot 11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

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Step 1.2.1

Multiply $16$ by $15$ .

$\frac{240 \cdot 14 \cdot 13 \cdot 12 \cdot 11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{1! (16 - 1!)} \cdot 0.23 \cdot {(0.77)}^{15}$

Step 1.2.2

Multiply $240$ by $14$ .

$\frac{3360 \cdot 13 \cdot 12 \cdot 11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{1! (16 - 1!)} \cdot 0.23 \cdot {(0.77)}^{15}$

Step 1.2.3

Multiply $3360$ by $13$ .

$\frac{43680 \cdot 12 \cdot 11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{1! (16 - 1!)} \cdot 0.23 \cdot {(0.77)}^{15}$

Step 1.2.4

Multiply $43680$ by $12$ .

$\frac{524160 \cdot 11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{1! (16 - 1!)} \cdot 0.23 \cdot {(0.77)}^{15}$

Step 1.2.5

Multiply $524160$ by $11$ .

$\frac{5765760 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{1! (16 - 1!)} \cdot 0.23 \cdot {(0.77)}^{15}$

Step 1.2.6

Multiply $5765760$ by $10$ .

$\frac{57657600 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{1! (16 - 1!)} \cdot 0.23 \cdot {(0.77)}^{15}$

Step 1.2.7

Multiply $57657600$ by $9$ .

$\frac{518918400 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{1! (16 - 1!)} \cdot 0.23 \cdot {(0.77)}^{15}$

Step 1.2.8

Multiply $518918400$ by $8$ .

$\frac{4151347200 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{1! (16 - 1!)} \cdot 0.23 \cdot {(0.77)}^{15}$

Step 1.2.9

Multiply $4151347200$ by $7$ .

$\frac{29059430400 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{1! (16 - 1!)} \cdot 0.23 \cdot {(0.77)}^{15}$

Step 1.2.10

Multiply $29059430400$ by $6$ .

$\frac{174356582400 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{1! (16 - 1!)} \cdot 0.23 \cdot {(0.77)}^{15}$

Step 1.2.11

Multiply $174356582400$ by $5$ .

$\frac{871782912000 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{1! (16 - 1!)} \cdot 0.23 \cdot {(0.77)}^{15}$

Step 1.2.12

Multiply $871782912000$ by $4$ .

$\frac{3487131648000 \cdot 3 \cdot 2 \cdot 1}{1! (16 - 1!)} \cdot 0.23 \cdot {(0.77)}^{15}$

Step 1.2.13

Multiply $3487131648000$ by $3$ .

$\frac{10461394944000 \cdot 2 \cdot 1}{1! (16 - 1!)} \cdot 0.23 \cdot {(0.77)}^{15}$

Step 1.2.14

Multiply $10461394944000$ by $2$ .

$\frac{20922789888000 \cdot 1}{1! (16 - 1!)} \cdot 0.23 \cdot {(0.77)}^{15}$

Step 1.2.15

Multiply $20922789888000$ by $1$ .

$\frac{20922789888000}{1! (16 - 1!)} \cdot 0.23 \cdot {(0.77)}^{15}$

Step 2

Simplify the denominator.

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Step 2.1

Expand $1!$ to $1$ .

$\frac{20922789888000}{1! (16 - 1 \cdot 1)} \cdot 0.23 \cdot {(0.77)}^{15}$

Step 2.2

Multiply $- 1$ by $1$ .

$\frac{20922789888000}{1! (16 - 1)} \cdot 0.23 \cdot {(0.77)}^{15}$

Step 2.3

Subtract $1$ from $16$ .

$\frac{20922789888000}{1! \cdot 15} \cdot 0.23 \cdot {(0.77)}^{15}$

Step 2.4

Expand $1!$ to $1$ .

$\frac{20922789888000}{1 \cdot 15} \cdot 0.23 \cdot {(0.77)}^{15}$

Step 2.5

Multiply $15$ by $1$ .

$\frac{20922789888000}{15} \cdot 0.23 \cdot {(0.77)}^{15}$

Step 3

Simplify the expression.

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Step 3.1

Divide $20922789888000$ by $15$ .

$1394852659200 \cdot 0.23 \cdot {(0.77)}^{15}$

Step 3.2

Multiply $1394852659200$ by $0.23$ .

$320816111616 \cdot {(0.77)}^{15}$

Step 3.3

Raise $0.77$ to the power of $15$ .

$320816111616 \cdot 0.01983174$

Step 3.4

Multiply $320816111616$ by $0.01983174$ .

$6362342556.03432065$