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=\frac{n!}{(n-r)!r!} \\ ^{50}C_6=\frac{50!}{(50-6)!6!} \end{gathered}$$\begin{gathered} ^{50}C_6=\frac{50!}{44!\times6!}=\frac{50\times49\times48\times47\times46\times45\times44!}{44!\times6\times5\times4\times3\times2\times1} \\ \\ \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