Question

probability
factorial expressions
evaluate.
6!3!
4!7!
simplify your answer as much as possible.

Explanation:

Step1: Expand factorials

Recall that \(n!=n\times(n - 1)\times\cdots\times1\). So \(6! = 6\times5\times4!\), \(7!=7\times6\times5\times4\times3\times2\times1\). Then \(\frac{6!3!}{4!7!}=\frac{6\times5\times4!\times3!}{4!\times7\times6\times5\times4\times3!}\).

Step2: Cancel out common terms

Cancel out \(4!\), \(6\), \(5\), and \(3!\) from the numerator and denominator. We get \(\frac{1}{7\times4}\).

Step3: Calculate the result

\(\frac{1}{7\times4}=\frac{1}{28}\).

Answer:

\(\frac{1}{28}\)