Question
Evaluate the factorial expression. \[ \frac{375!}{374!} \] \( \frac{375!}{374!}=\square \)
Ask by Parry Henry. in the United States
Mar 18,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( \frac{375!}{374!} = 375 \)
Solution
Calculate or simplify the expression \( \frac{375!}{374!} \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{375!}{374!}\)
- step1: Expand the expression:
\(\frac{375\times 374!}{374!}\)
- step2: Reduce the fraction:
\(375\)
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Simplify this solution Mind Expander
To evaluate the expression \( \frac{375!}{374!} \), we can simplify it using the definition of factorial. The factorial \( n! \) is the product of all positive integers up to \( n \). Therefore: \[ 375! = 375 \times 374 \times 373 \times \ldots \times 1 \] \[ 374! = 374 \times 373 \times \ldots \times 1 \] When we substitute \( 375! \) into the expression, we can cancel out \( 374! \) in the numerator and the denominator: \[ \frac{375!}{374!} = \frac{375 \times 374!}{374!} = 375 \] So, \[ \frac{375!}{374!} = 375 \]
