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:

$^nC_r=\frac{n!}{r!(n-r)!}$

Applying this, we get:

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

Therefore, the required number of ways are 10737573.