Evaluate the factorial expression. \( \frac{20!}{16!} \) \( \frac{20!}{16!}=\square \)
Upstudy AI Solution
Answer
Solution

Sign in to Unlock Answers for Free!
A Learning Platform Trusted by Millions of Real Students and Teachers.

Answered by UpStudy AI and reviewed by a Professional Tutor
Extra Insights
To simplify \( \frac{20!}{16!} \), we can express \( 20! \) as \( 20 \times 19 \times 18 \times 17 \times 16! \). This allows us to cancel the \( 16! \) from the numerator and denominator. So, we have: \[ \frac{20!}{16!} = \frac{20 \times 19 \times 18 \times 17 \times 16!}{16!} = 20 \times 19 \times 18 \times 17 \] Now, calculating that gives us: \( 20 \times 19 = 380 \) \( 380 \times 18 = 6840 \) \( 6840 \times 17 = 116280 \) Thus, \( \frac{20!}{16!} = 116280 \) or written in the box: \[ \frac{20!}{16!}=\boxed{116280} \]