Question

from a club of 20 people, in how many ways can a group of six members be selected to attend a conference?
a group of 6 members can be selected to attend a conference in \\(\square\\) ways.

Explanation:

Step1: Use the combination formula

The combination formula is \(C(n,r)=\frac{n!}{r!(n - r)!}\), where \(n = 20\) (total number of people) and \(r=6\) (number of people to be selected).

Step2: Calculate factorial values

\(n!=20! = 20\times19\times18\times17\times16\times15\times14!\)
\(r!=6!=6\times5\times4\times3\times2\times1 = 720\)
\((n - r)!=(20 - 6)!=14!\)

Step3: Substitute into the formula

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Answer:

\(38760\)