Question

20. A local children's center has 47 children enrolled, and 6 are selected to take a picture for the center's advertisement. How many ways are there to select the 6 children for the picture?

Answer 1

Given:

Total number of children enrolled = 47

Number of children to be selected = 6

Number of ways to select 6 children for the picture are:

`=^(47)C_6`

Formula for combination is given as:

`^nC_r=(n!)/(r!(n-r)!)`

Applying this, we get:

`\begin{gathered} ^(47)C_6=(47!)/(6!(47-6)!) \\ =(47!)/(6!41!) \\ =10737573 \end{gathered}`

Therefore, the required number of ways are 10737573.