Probability question.

[Lior]

Hi all,

I trying to solve this probability question:

Its a about a lottery game.

I choose 7 different numbers from range of 1 to 70.
The lottery directors choose 17 different numbers from the range of 1 to 70.

What are the chances that all of the 7 numbers I chose are included within the 17 numbers the Directors chose?

Remark: A number cannot be chosen more than once. I mean, after I chose my first number, I have to pick up more 6 numbers out of the 69 left etc... and so about the directors, after they chose their first number, they have to pick up more 16 numbers from the 69 numbers left etc...

Thanks.

[Guv]

Combinations(70, 17) = 70! / 53!17!, which is the total number of possibilities.

Combinations(63, 10) = 63! / 53!10!, which is the number of possibilities including the 7 numbers you picked. Any combination of the remaining 63 numbers can be used along with your 7 numbers.

Divide the above to get probability or odds.

Probability = .000 016 223

Odds = One chance in 61,640 or 61,639 to one.

The above does not seem to be a real high odds lottery like some of those run by various states. I used my HP calculator, but there is so much cancellation of factors possible, that it is not difficult to calculate the above by hand.

[Lior]

The lottery above is ran nowadays in Israel.

It's a new one.

each guess of 7 numbers costs 7 nis, and if you hit the whole 7 numbers the directors chose, you get back 70,000 nis.

Nis=New Israeli Shekel

[Guv]

That makes the odds I calculated seem about right. Typical ripoff by government organizations.

Odds 61,639 to one; Payoff 10,000 for one.

MY local bookie used to pay 500-700 to one when odds were 999 to one on 3-digits numbers. That was called criminal by our government.