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=\frac{n!}{(n-x)!x!}$

Then applying the formula for combination above we have

$^{46}C_6=\frac{46!}{(46-6)!6!}=\frac{46!}{40!6!}=9366819$

Therefore, there are about 9366819 six numbers