what is the probabilty of winning the lottery if the balls are # 1-54 & you have to get 6 right?

Answer 1

Assuming the balls aren't put back into the ball selector, there are 54 choices for the first ball, 53 choices for the second ball, 52 choices for the third ball, etc.

If you have to guess the numbers in the correct order, your chances of winning are
1 in (54*53*52*51*50*49)
= 1 in 18,595,558,800
or about 1 in 19 billion.

If you only need to guess the correct numbers, and order doesn't matter, your chances of winning are
1 in (54 choose 6)
= 1 in 25,827,165
or about 1 in 26 million.

Answer 2

This is the probability of winning if the numbers have to be in order:

In order to get 1 number correct, the chances are 1 in 54, or:

1/54

Next, to get another one right, the chances are 1 in 53:

1/53

This pattern continues until you need to get the 6th one right:

1/52 <=== 3rd ball
1/51 <=== 4th ball
1/50 <=== 5th ball
1/49 <=== 6th ball

Now, in order to find the probablity of drawing all of these six balls, multiply these fractions:

1/54 * 1/53 * 1/52 * 1/51 * 1/50 * 1/49
= 1/18595558800

This is your answer.

Otherwise, if they do not have to be in order:

The probability would be:

1/(54 combination 6)

(54 combination 6 is the chances of choosing 6 items in a total of 54 items)

This combination, 54 combination 6, is equal to:

(54 * 53 * 52 * 51 * 50 * 49)/(6 * 5 * 4 * 3 * 2 * 1)
= 25827165

So the probablity of this is:

1/25827165

This answer and the one mentioned before are the two possible answers, depending on what you meant.

Hope this helps!

Answer 3

If I am reading the question right...You already have 6 numbers and you need just one more. As you might have guessed your odds are now perty good when compared to the first drawing.

Your odds are now 1 in 54

Look at it like this: there are 54 balls and you can pick one number. there are 53 other people who can also pick 1 number. the odds are 100% that someone picked the right number. the odds that it was you were 1 in 54

Each time you pick a right number for a group of numbers the odds increase in your favor that the next number you picked will be the right number.

Answer 4

1 in (54 choose 6) = 1 in 25827165

Answer 5

n! / r!(n-r)! is the required formula for this problem where n=the range of the ball number i.e 54 and r=number of balls i.e. 6 so its 1/25827165

Answer 6

54C6 = 54!/((54-6)! 6!) = 25,827,165

Answer 7

Still not as good as getting hit by lightning or experiencing a California earthquake.