Question

you volunteer to help drive children at a charity event to the zoo, but you can fit only 6 of the 20 children present in your van. how many different groups of 6 children can you drive? how many different groups of 6 children can you drive?

Explanation:

Step1: Identify the combination formula

The formula for combinations is \(C(n,r)=\frac{n!}{r!(n - r)!}\), where \(n = 20\) (total number of children) and \(r=6\) (number of children to be chosen).

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:

\(38760\)