The odds on lotto 14 MILLION TO 1 (6 FROM 49) HOW IS THIS FIGURE WORKED OUT?

Answer 1

The Jackpot - 6 Numbers
6 numbers are drawn at random from the set of integers between 1 and 49, which means there are 49!/(6!*(49-6)!) combinations of numbers - this means that the jackpot chance is 1 in 13,983,816 or approximately 1 in 14 million.

5 Numbers + Bonus Number
You are still matching 6 numbers from the 1 to 49 set as above, but you can now do it in 6 different ways (by dropping each of the main numbers in turn), therefore the chance is 1 in 13,983,816/6, which works out as 1 in 2,330,636.

5 Numbers
This is 42 times more likely than getting 5 numbers + the bonus number - the chance is 1 in 2,330,636/42, which evaluates to 1 in 55,491.33333.

4 Numbers
Firstly, let's take the case of the first 4 of your numbers matching and the last 2 not matching.
In this single case (where each set of chances relies on the previous event occurring):

Chance that your 1st number matches a winning lottery number is 1 in 49/6.
Chance that your 2nd number matches a winning lottery number is 1 in 48/5.
Chance that your 3rd number matches a winning lottery number is 1 in 47/4.
Chance that your 4th number matches a winning lottery number is 1 in 46/3.
Chance that your 5th number doesn't match a winning number is 1 in 45/(45-2) [because there are still 2 unmatched winning numbers].
Chance that your 6th number doesn't match a winning number is 1 in 44/(44-2) [yes, still 2 unmatched winning numbers].

Now you need to accumulate all those chances by multiplying them together:
1 in (49/6)*(48/5)*(47/4)*(46/3)*(45/43)*(44/42) which is 1 in 15486.953.
Now this is the chance for that single case occurring, but there are 15 combinations of matching 4 from 6, so you divide the answer by 15 to get 1 in 15486.953/15 or 1 in 1032.4.

3 Numbers
Follow exactly the same scheme as the 4 match above to get these figures:
1 in (49/6)*(48/5)*(47/4)*(46/43)*(45/42)*(44/41) (which is 1 in 1133.119) for a single case.
There are 20 combinations of 3 from 6, so the chance of a 3 match is 1 in 1133.119/20 or 1 in 56.7.
Now you know why we're still skint!!

Answer 2

6 FROM 49 = 49*48*47*46*45*44/ (6*5*4*3*2*1)=13983816
This is almost 14 million to 1. There of 49 ways of choosing the first number, 48 ways of choosing the second number(because there are only 48 balls left) and 47 ways of choosing the third number etc.
The next bit is difficult to grasp. The six numbered balls could have been chosen in any one of ( 6*5*5*4*3*2*1) ways without making one iota of difference to the result. The numbers: 7,13,41,32,17, 11;
can be rearranged 720 different way.....yet they are still the winning combination, so the 49*48*47*46*45*44 must be divided by 720(6!).
True, it's difficult to grasp this!

Answer 3

pick 6 numbers.

#1 - 49 choices
#2 - 48 choices
#3 - 47 choices
#4 - 46 choices
#5 - 45 choices
#6 - 44 choices

Total = 49 x 48 x 47 x 46 x 45 x 44 = 10 billion

But since the numbers can be in any order (ie, it doesn't matter if the number 23 is the 3rd number drawn or the 5th number drawn, just that it is drawn), you have to divide by the combination numbers

6 spots so = 6 x 5x 4x 3 x 2 x 1 = 720

10 billion divided by 720 = 14 million

Answer 4

Assume there are 49 balls, and we need to choose 6. In order to find the odds of winning on a single lottery ticket , we first need to find the size of sample.

The sample, in this case, is the number of possible combinations of 49 numbers we can make with using 6 at a time, with no repeating.

Therefore:

First #: 49 ways to choose:
2nd #: 48 ways to choose
3rd: 47 ways to choose
4th 46
5 45
4 44

Therefore, size of the sample is (49*48*47*46*45*44), or we could call this value simply 49! / 43! [ ! = factorial ]

chances of winning on a single ticket is therefore

1 in [ 49! / 43! ] = 1 in 13,983,816

You can quickly compute this as: 49 choose 6:

Answer 5

The formula is 49!/(6! x 43!)
where 49! = 49x48x47x46x45x44 x 43 x------1
and 43! = 43x42x41x40x---------1
6! = 6x5x4x3x2x1
49!/(6! x 43!) =
(49x48x47x46x45x44x43x42 -------1) / (43x42x42x40 ----1)(6x5x4x3x2x1)
Cancel to obtain:-
49x48x47x46x45x44/(6x5x4x3x2x1) = 13983816
Alternatively if you have a Mathematics calculator, you may calculate
49!/(6!x43!) by utilising the ! button on the calculator.
Note that upon rounding 13983816 becomes 14,000,000

Answer 6

Number of Combinations = 49! / 6! (49-6)!
= 49! / (6! x 43!)
= (approx.) 14 million

Answer 7

49x48x47x46x45x44 divided by 6x5x4x3x2x1
you take the highest of the 2 numbers (6 and 49) and multiply the top ( in this case )6 together then multiply the bottom 6 and divide one result by the other
so 3 from 4 would be 4x3x2 divided by 3x2x1 = 4

Answer 8

Take 49! (49*48*47....*3*2*1) and divide that by (49-6)!(6!)

(49*48*47*46*45*44)/6*5*4*3*2 = 13,983,816

Answer 9

The number of possible lotto choices is 49 C 6=(49!)/((6!)*(43!)) which is about 14,000,000.

Answer 10

Look up on the internet about factorials, and permutations and combinations...you have to work out how many time 6 numbers can be chosen from 49...as you can imagine...there are many, many, many combinations!