Question

In a State lottery, how many different combinations of 6 numbers can be obtained from a total of 46 numbers? b) In how many different sequences can we select 10 racecars out of 36 racecars?

Answer 1

SOLUTION (a)

There are 46 numbers and to select a combination of 6 numbers

Hence, we have a combination

`^(46)C_6`
`^nC_x=(n!)/((n-x)!x!)`

Then applying the formula for combination above we have

`^(46)C_6=(46!)/((46-6)!6!)=(46!)/(40!6!)=9366819`

Therefore, there are about 9366819 six numbers