Question

A lottery game requires that you pick 6 different numbers from 1 to 84 . If you pick all 6 winning​ numbers, you win the jackpot. If you pick 5 of the 6 numbers​ correctly, you win ​$300,000 . In how many ways can you pick exactly 5 of the 6 winning numbers without regard to​ order?

Answer 1

Answer:

There is 2,348,889,264 way to pick exactly 5 out of the 6 winning numbers.

Explanation:

hi, we need to use a combination in order to get 5 out of the 6 winning numbers of a ticket without regard to order. The formula is as follows.

$C(n,r)=\frac{n!}{r!(n-r)!}$

Where:

n = total numbers in the lottery (in our case, 84)

r = winning numbers (in our case, 5)

everything should look like this:

$C(n,r)=\frac{84!}{5!(84-5)!}$

$C(n,r)=\frac{84!}{5!(79)!}$

$C(n,r)=\frac{84*83*82*81*80}{5*4*3*2}=2,348,889,264$

Best of luck.