In a Lotto game with 56 numbers to choose from how many single tickets would i need to buy to win?

Question

what i mean is how many different number combinations can you get out of 56 different numbers how would you calculate this in lamens terms

Answer 1

Yes, the number of tickets required to ensure winning the jackpot will depend on the number of numbers(balls) which are drawn. For a 6 / 56 lottery, the number of tickets is 32,468,436. If it is a 7 / 56, then the number of tickets is 231,917,400.

As far as calculating it in laymen's terms: If you have a 6 / 56 lottery then chances of the first number drawn matching one of your 6 numbers is 6/56. The chances of the 2nd number drawn matching one of your five remaining numbers is 5/55 (since the balls are not replaced). The chance of the 3rd number drawn matching one of your 4 remaining numbers is 4/54 and so on...If you have one ticket, the chances of you winning the jackpot in the 6 / 56 is therefore:

6/56 x 5/55 x 4/54 x 3/53 x 2/52 x 1/51 = 1 in 32,468,436

So you need to buy 32,468,436 tickets to cover all the possibilities. The number of tickets required is just the inverse of the product of the above fractions. That is the number of tickets

= 56/6 x 55/5 x 54/4 x 53/3 x 52/2 x 51 = 32,468,436

The above product could be rewritten as:

(56x55x54x53x52x51) / (6x5x4x3x2x1)

In mathematical notation this equals 56! /(56-6)!6!
where, for example, 6! = 6x5x4x3x2x1 = 720

In general, if you are choosing r distinct numbers (or objects)
from n distinct numbers (or objects) then the number of distinct combinations (tickets in your case) is given by n!/(n-r)!r!, and it is usually denoted by "nCr" (Of course n is greater than or equal to r).

Here is a link to a lottery odds calculator:

http://www.csgnetwork.com/oddscalc.html

Answer 2

It depends on how many numbers you will choose.
In this case we let n = number of numbers to choose.

In a normal lotto game the order of the numbers is not important.

The formula for the number of combinations of n taken r things at a time is
nCr = n!/(n - r)!r!
With 56 numbers to choose from and n numbers to choose, the possible number of combinations is
56Cn = 56!/(56 - n!)n!

That is the answer, for n numbers to choose. If I let n = 6, then the number of combinations(choosing 6 numbers from 56 numbers is)
56!/(56 - 6)!6!
= 56!/50!6!
= 56 · 55 · 54 · 53 · 52 · 51/(6 · 5 · 4 · 3 · 2 · 1)
= 14 · 11 · 9 · 53 · 26 · 17
= 32,468,436 possible combinations for 6 numbers

^_^

Answer 3

Assuming to win you need to match 6 balls you would need to buy 32,468,436 tickets.

It is done using "n choose r" which in your case is "56 choose 6"

"n choose r" = n! / ((n - r)! x r!)

So to win your lottery it is 56! / (50! x 6!)

6! pronounced "6 factorial" is 6 x 5 x 4 x 3 x 2 x 1

So 56! is 56 x 55 x 54 x ... x 3 x 2 x 1

If you have 6 numbers on your ticket and want to calculate the odds of getting 5 numbers correct, it is not just simply "56 choose 5". You also have to take into account the one ball that isn't correct.

Seeing as how you want this in laymans terms, I suggest you see if you understand getting all 6 correct first before moving onto 1, 2, 3, 4 or 5 correct.

Answer 4

I'm getting a different number when I do the math.

The number of combinations of 6 numbers out of 56 possibilities is 56! / [(56-6)! x 6!], or 56 x 55 x 54 x 53 x 52 x 51 / (6 x 5 x 4 x 3 x 2 x 1) = 32,468,436 possible ways of filling out the lottery ticket.

Answer 5

7.10999E+74 to match all 56 numbers.
(That's 710,999 followed by 69 zeros)
To match one number it is a 1 in 56 chance.
To match two numbers it would be 1 in 3080 chance (56 numbers times the 55 remaining numbers).
To match three numbers it would be 1 in 166320 chance (56 numbers times 55 numbers times 54 numbers)

Since the same number can't be picked twice (with the exception of a lottery where the "special" number is chosen from a different batch of balls from the first set of numbers), you just multiply on a reducing scale 56*55*54*53..., each iteration representing a pick. 6 numbers equals 6 iterations, five require five etc...

Answer 6

How many numbers do you pick, the result is different if you pick 5 or 6. For 6 with 56 numbers it would be approx 17,000,000. One do you have that investment, two would you be the only winner, and three even at say 5 seconds to check a row of numbers, it would take approx 6 months non stop to check them all. So, is it worth it?

Answer 7

56! / 50!6! = 32,468,436 to 1 odds against winning. You need to buy 32,468,436 tickets to ensure winning. Good luck finding someone who can sell you this many tickets!

This is assuming that the Lotto is not PowerBall-like, with a special ball selected from a different set of balls. I also am assuming that six winning numbers are selected.

Answer 8

If that Lotto draws 6 numbers, its 56C6 which is 32,468,436. I did this on my calculator using the nCr function.