Question

There 14 lottery tickets and 6 of them are lucky(you can win something). How many ways are there to 2 lucky tickets, if you can take 5 of 14. (the answer is 85). Any tips?

Answer 1

to take 2 lucky tickets*

Answer 2

@Mertsj

Answer 3

i can try to rewrite a problem, if you dont understand what i need to get

Answer 4

Try, then :)

Answer 5

There is 14 lottery tickets and 6 of them are lucky (you can win something). Dou you understand this?

Answer 6

Yes...

Answer 7

so, you pick 5 of 14 tickets. Understandable?

Answer 8

Yes.

Answer 9

How many ways are to pick that 5 tickets, if there must be 2 lucky ones?

Answer 10

the answer is 85, if it helps.

Answer 11

At least 2, or only 2?

Answer 12

only

Answer 13

oh, and i gave wrong answer, it is 840

Answer 14

:/

Answer 15

://

Answer 16

Well, It was hard earlier, because you said the answer was 85... which seemed too small.

Answer 17

so,is it easier now?

Answer 18

Much.

Answer 19

It's basically the product of how many ways you can pick two lucky tickets and how many ways you can pick three not-lucky tickets :)

Answer 20

Can you explain me step by step? I still dont get it :/

Answer 21

Well, you are going to pick five tickets, and you want to know how many ways you can pick a combination of five where exactly two are lucky, right?

Well, that means exactly three are not-lucky.

Answer 22

\[C^6_2\times C^{14-6}_3=\frac{6\times5\times\cancel{4!}}{\cancel{4!}\times2}\times\frac{8\times7\times6\times\cancel{5!}}{\cancel{5!}\times3\times2}=840\]

Answer 23

So, it boils down to how many ways you can pick two lucky tickets, and there are 6 of them.
So it'd be 6C2

Answer 24

times...
the number of ways you can pick three not-lucky tickets, and there are 8 of them.
So it'd be
8C3

Answer 25

oh, okay! Thank you a lot! I have another problem, with "at least", what is different about it?

Answer 26

We'll see :P