Answer :
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:
[tex]nCr =\frac{n!}{(n - r)! . r !}[/tex]
[tex]6C5=\frac{6!}{(6-5)! . 5!}[/tex]
[tex]6C5=\frac{6!}{(1)! . 5!}[/tex]
[tex]6C5=\frac{6.5.4.3.2.1}{1.5.4.3.2.1}[/tex]
[tex]6C5=\frac{6}{1}[/tex]
[tex]6C5= 6 \ ways[/tex]
∴ 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:
[tex]nCr =\frac{n!}{(n - r)! . r !}[/tex]
[tex]6C4=\frac{6!}{(6-4)! . 4!}[/tex]
[tex]6C4=\frac{6!}{(2)! . 4!}[/tex]
[tex]6C4=\frac{6.5.4.3.2.1}{2.1.4.3.2.1}[/tex]
[tex]6C4=\frac{30}{2}[/tex]
[tex]6C4= 15 \ ways[/tex]
∴ 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:
[tex]nCr =\frac{n!}{(n - r)! . r !}[/tex]
[tex]6C3=\frac{6!}{(6-3)! . 3!}[/tex]
[tex]6C3=\frac{6!}{(3)! . 3!}[/tex]
[tex]6C3=\frac{6.5.4.3.2.1}{3.2.1.3.2.1}[/tex]
[tex]6C3=\frac{120}{6}[/tex]
[tex]6C3= 20 \ ways[/tex]
∴ 20 ways are to match 3 of 6 numbers
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