Question

how many ways are there to win the jackpot? how many ways are there to match 5 of 6 numbers? how many ways are there to match 4 of 6 numbers? how many ways are there to match 3 of 6 numbers?

Answer 1

The number of ways to  match 5 of 6 numbers is 6 ways

The number of ways to  match 4 of 6 numbers is 15 ways

The number of ways to  match 3 of 6 numbers is 20 ways

To calculate number of ways to match 5 of 6 numbers we have to use to formula:

$nCr =\frac{n!}{(n - r)! . r !}$

$6C5=\frac{6!}{(6-5)! . 5!}$

$6C5=\frac{6!}{(1)! . 5!}$

$6C5=\frac{6.5.4.3.2.1}{1.5.4.3.2.1}$

$6C5=\frac{6}{1}$

$6C5= 6 \ ways$

∴ 6 ways are to match 5 of 6 numbers

To calculate number of ways to match 4 of 6 numbers we have to use to formula:

$nCr =\frac{n!}{(n - r)! . r !}$

$6C4=\frac{6!}{(6-4)! . 4!}$

$6C4=\frac{6!}{(2)! . 4!}$

$6C4=\frac{6.5.4.3.2.1}{2.1.4.3.2.1}$

$6C4=\frac{30}{2}$

$6C4= 15 \ ways$

∴ 15 ways are to match 4 of 6 numbers

To calculate number of ways to match 4 of 6 numbers we have to use to formula:

$nCr =\frac{n!}{(n - r)! . r !}$

$6C3=\frac{6!}{(6-3)! . 3!}$

$6C3=\frac{6!}{(3)! . 3!}$

$6C3=\frac{6.5.4.3.2.1}{3.2.1.3.2.1}$

$6C3=\frac{120}{6}$

$6C3= 20 \ ways$

∴ 20 ways are to match 3 of 6 numbers

Learn more about Jackpots here :

brainly.com/question/27116420

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