Question

1. find the value of \\(\dbinom{8}{7}\\). \\(\dbinom{8}{7} = \text{enter your next step here}\\)

Explanation:

Step1: Recall the combination formula

The combination formula is \(\binom{n}{r}=\frac{n!}{r!(n - r)!}\), where \(n = 8\) and \(r=7\).

Step2: Substitute the values into the formula

\(\binom{8}{7}=\frac{8!}{7!(8 - 7)!}=\frac{8!}{7!1!}\)

Step3: Simplify the factorials

We know that \(n!=n\times(n - 1)!\), so \(8!=8\times7!\). Then \(\frac{8\times7!}{7!1!}\). The \(7!\) terms cancel out, and \(1!=1\), so we have \(\frac{8\times1}{1}=8\).

Answer:

\(8\)