A state Lottery is designed so that a player chooses six numbers from 1 to 30 on one lottery ticket.?

Question

What is the probability that a player with one lottery ticket will win? What is the probability of winning if 100 different lottery tickets are purchased?

Answer 1

1 in 593,775. If you purchase 100 tickets, your odds are 100 in 593,775.

The general formula for picking n numbers from a group of m numbers is:

mCn = m!/(n!*(m-n)!).
In this case (30C6) = 30!/(24!*6!) = 593,775

Answer 2

The the odds of a single ticket being a winner are:
1 in 593,775
or
0.0000016841

If you bought 100 tickets you would have a chance of 1 in 5,937.75 of winning.

If you're interested in the calculation; it is as follows.
A single ticket has 6 different numbers from 1-30 on it which must match all 6 drawn in order to win.

For the first number to match; it can match any of your 6 numbers from 30 possible choices. So 6/30 chance.

For the second number to match; it can match any of your 5 remaining numbers from 29 possible choices. So 5/29 chance.

For the third number to match; it can match any of your 4 remaining numbers from 28 possible choices. So 4/28.

For the fouth number; it's 3/27

For the fifth number it's 2/26

For the sixth and final number it's 1/25.

Since all of these probabilities must happen in sequence; we multiply the odds of each event together.

(6/30) * (5/29) * (4/28) * (3/27) * (2/26) * (1/25)

Which gives us 1/593775 chance of any random ticket being a winner.