# What are the odds of winning Toto?

## TOTO Odds

#### Recall (from the Combinations section) that the number of ways in which r objects can be selected from a set of n objects, where repetition is not allowed, is given by:

Crn=n!r!(n−r)!\displaystyle{{C}_{{r}}^{{n}}}=\frac{{{n}!}}{{{r}!{\left({n}-{r}\right)}!}}

#### The odds of winning the top Group 1 prize are 1\displaystyle{1} in C(49,6). That is:

1C(49,6)=113,983,816\displaystyle\frac{1}{{{C}{\left({49},{6}\right)}}}=\frac{1}{{{13},{983},{816}}}

=7.15×10−8\displaystyle={7.15}\times{10}^{ -{{8}}}