How many tickets can I get by selecting 6 numbers from 1 to 40 for each play.?

Question

Can anybody tell me that how many tickets (1 ticket should contain 6 different and unique numbers from 1 to 40) will be total, if u pick 6 numbers from 1 to 40 and numbers shouldn't be identical ? Each number should be unique.like 1,2,3...not like 1,1,1,3..... For example. if we need to pick 2 numbers from 1 to 4 to win, we can make total 6 sets picking by 2 numbers from 1 to 4.. and we can buy 6 tickets by selecting 2 numbers from 1 to 4 like this: 1,2------1,3------1,4----------2,3-----2... Non of numbers r missing from the range of 1 to 4..so how many sets will be made by picking 6 unique numbers from 1 to 40 as we picked 2 unique numbers from 1 to 4 for each play?? I must say that person will be most intelligent who gives me answer of this question..

Answer 1

The answer is

(40 x 39 x 38 x 37 x 36 x 35) / (6 x 5 x 4 x 3 x 2 x 1)

=  2,763,633,600 / 720

=  3,838,380

This is pretty basic statistics. I am not how well I can explain why it is true, but I'll give it a try. Suppose the six winning numbers has already been chosen and you wanted to calculate the odds of picking the winning numbers. The odds that the first number you pick would be one of the six numbers would be 6 / 40. Assuming the first number matched, the odds that the second number you pick would be one of the five remaining numbers would b 5 / 39. Continue this process and you get the odds of picking the winning all six numbers are

(6 / 40) x (5 / 39) x (4 / 38) x (3 / 37) x (2 / 36) x (1 / 35)

which works out to 1 / 3,838,380.

That means the total number total possible number of combinations is 3,838,380.

If you want verification that this method is correct, repeat the process with 47 numbers instead of 40. The answer you get will match the number at

http://michigan.gov/lottery/0,1607,7-110...