Question

The state of California has a Super Lotto drawing twice a week in which 6numbers 1 through 50) are drawn at random. How many ways are 6numbers drawn?

Answer 1

This is a question on combination.

The number of ways 6 numbers can be drawn from 50 numbers is given by;

`\begin{gathered} ^nC_r=(n!)/((n-r)!r!) \\ ^(50)C_6=(50!)/((50-6)!6!) \end{gathered}`
`\begin{gathered} ^(50)C_6=(50!)/(44!*6!)=(50*49*48*47*46*45*44!)/(44!*6*5*4*3*2*1) \\ \\ \text{Cutting out the common factors out, we will be left with} \\ =\text{ 15,890,700} \end{gathered}`

Therefore, the number of ways it can be drawn every twice in a week is 15,890,700 ways