QuestionCalculate $\frac{7 !}{15 !}$ . Choose the correct answer: a. 0.00000000384, b. 3.85, c. 384000000000, d. 0.000000000384.

Studdy Solution

STEP 1

Assumptions1. The "!" symbol denotes factorial, which is the product of all positive integers up to a given number. . The expression $\frac{7 !}{15 !}$ is asking us to divide the factorial of7 by the factorial of15.

STEP 2

First, let's write out the factorial of7 and15.
$7! =7 \times6 \times5 \times4 \times \times2 \times1$ $15! =15 \times14 \times13 \times12 \times11 \times10 \times9 \times8 \times7 \times6 \times5 \times4 \times \times2 \times1$

STEP 3

We can simplify the expression by cancelling out the common terms in the numerator and the denominator.
$\frac{7 !}{15 !} = \frac{7 \times6 \times5 \times \times3 \times2 \times1}{15 \times14 \times13 \times12 \times11 \times10 \times9 \times8 \times7 \times6 \times5 \times \times3 \times2 \times1} = \frac{1}{15 \times14 \times13 \times12 \times11 \times10 \times9 \times8}$

STEP 4

Now, we can calculate the value of the expression.
$\frac{1}{15 \times14 \times13 \times12 \times11 \times10 \times9 \times8} =0.000000000384$ So, the correct answer is d.0.000000000384.

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