Question

you volunteer to help drive children at a charity event to the zoo, but you can fit only 6 of the 16 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 number of combinations of \(n\) objects taken \(r\) at a time is given by \(C(n,r)=\frac{n!}{r!(n - r)!}\), where \(n = 16\) (total number of children) and \(r=6\) (number of children in each group).

Step2: Calculate factorial values

\(n!=16! = 16\times15\times14\times13\times12\times11\times10\times9\times8\times7\times6\times5\times4\times3\times2\times1\)
\(r!=6! = 6\times5\times4\times3\times2\times1\)
\((n - r)!=(16 - 6)!=10! = 10\times9\times8\times7\times6\times5\times4\times3\times2\times1\)

Step3: Substitute into the formula

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Answer:

\(8008\)