Question

7.6
score: 3/19 answered: 3/19
question 4
evaluate the expression.
\\(\dbinom{100}{100}\\)
question help: video ebook
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Explanation:

Step1: Recall the combination formula

The binomial coefficient \(\binom{n}{k}\) (read as "n choose k") is given by the formula \(\binom{n}{k}=\frac{n!}{k!(n - k)!}\), where \(n!=n\times(n - 1)\times\cdots\times1\) for \(n\geq1\) and \(0!=1\).

Step2: Substitute \(n = 100\) and \(k = 100\) into the formula

For \(\binom{100}{100}\), we have \(n = 100\) and \(k = 100\). So,

$$
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Since \(0!=1\) and \(\frac{100!}{100!}=1\), we get \(\frac{1}{1\times1}=1\).

Answer:

\(1\)