Question

Find the value of \(\frac{9 !}{4 !}\).

Short answer

Answer: The value of \(\frac{9 !}{4 !}\) is 15120.

Step-by-step solution

Understanding Factorial

Factorial is a mathematical term represented by the symbol "!", which means to multiply a given number by all the positive whole numbers smaller than the given number. For example, \(4! = 4 \times 3 \times 2 \times 1 = 24\).

Evaluating the Factorials

Now that we know the factorial concept, we can evaluate the factorials for both numbers in the expression. \(9! = 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 362880\) \(4! = 4 \times 3 \times 2 \times 1 = 24\)

Dividing the Factorials

Finally, we'll divide the two factorial values we calculated to find the answer. \(\frac{9 !}{4 !} = \frac{362880}{24} = 15120\) So, the value of \(\frac{9 !}{4 !}\) is 15120.