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Chapter 11: Problem 31

Evaluate each factorial expression. \(\frac{13 !}{(13-3) !}\)

Short Answer

Expert verified
The evaluated factorial expression \( \frac{13 !}{(13-3) !} \) is 1716.

Step by step solution

01

Understanding Factorial Operations

The factorial of a number \( n \) is the product of all positive integers less than or equal to \( n \). It鈥檚 denoted by \( n ! \). So, \( 13! = 13 脳 12 脳 11 脳 10 脳 9 脳 8 脳 7 脳 6 脳 5 脳 4 脳 3 脳 2 脳 1 \) and similarly for other numbers.
02

Simplify the Expression

To simplify this expression, \( \frac{13 !}{(13-3) !} \), we first compute the expression inside the parentheses, which is \( 13 - 3 = 10 \). Thus, the expression now becomes \( \frac{13 !}{10 !} \). As both 13! and 10! shares common factors from 10 down to 1, these numbers can be factored out on both the numerator and the denominator, leaving us with \( 13 脳 12 脳 11 \).
03

Compute the Resulting Expression

Next we multiply the remaining integers, which yields \( 13 脳 12 脳 11 = 1716 \). Thus, \( \frac{13 !}{10 !} = 1716 \).

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