Question

I'm sort of not sure on this lotto probability problem.
Out 54 numbers (1 to 54), to win the second price, you just need to have 5 matching numbers. What is the probability of winning the second price?

Answer 1

you pick 6 numbers btw

Answer 2

I was thinking (6C5) (48) / (54C6)

Answer 3

huhm... I got a metal. Must be right XD

Answer 4

Hmmm...

Answer 5

looks correct to me

Answer 6

How many numbers do you get to pick?

Answer 7

6

Answer 8

no repeated number then?

Answer 9

can't pick 1, 1, 1, 1, 1, 1?

Answer 10

numbers can not be repeated

Answer 11

u pick 5 correct, and u pick one incorrect :
total favorable combinations for 2nd prize = 6c5 * 48c1

Answer 12

does that look right ?

Answer 13

well, that's what I did. But wasn't sure

Answer 14

Since \({54}\choose {6}\) is correct for total possibilities, it comes down to counting wins. How did you come up with what you got?

Answer 15

suppose the winning number is 123456, then any 5 of these numbers can got with the other 48 numbers (can't go with the numbers that already appeared in the winning number. That's why there is 48 of them)
so (6C5) (48C1)

It sounds convincing to me though...

Answer 16

The first time I tried this, I got it totally wrong :D

Answer 17

Ah,, 6C5 * (54-6)C1, hmmm

Answer 18

so far I don't see a flaw.

Answer 19

yea, it's difficult to be 100% sure when there are so many possible outcomes. But with you guys' comments, i'm 99.99% sure it is correct XD.

Answer 20

just to convince a bit more, we can reduce 54 to 7 and consider the probability

Answer 21

7 numbers :

winning numbers : 123456

total : 7c6 ways
fvorable : 6c5 * 1c1 = 6
probability = 6/7

which looks good...

Answer 22

indeed :) thanks for the comments

Answer 23

np :)