Question

A local children's center has 46 children enrolled, and 6 are selected to take a picture for the center'sadvertisement. How many ways are there to select the 6 children for the picture?

Answer 1

The question requires us to find how many ways we can select 6 children from a total of 46.

The formula for combinations is given as follows;

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

Where n = total number of children, and r = number of children to be selected. The combination now becomes;

`\begin{gathered} 46C_6=(46!)/((46-6)!6!) \\ 46C_6=(46!)/(40!*6!) \\ 46C_6=(5.5026221598*10^(57))/(8.1591528325*10^(47)*720) \\ 46C_6=(5.5026221598*10^(10))/(8.1591528325*720) \\ 46C_6=(0.674410967996781*10^(10))/(720) \\ 46C_6=(6744109679.967807)/(720) \\ 46C_6=9,366,818.999955287 \\ 46C_6=9,366,819\text{ (rounded to the nearest whole number)} \end{gathered}`