Twice a week, the State of Michigan runs a 6 out of 49 number lotto that pays at least $2 million. The State needs to know the probabilities of winning in order to ensure that the lottery has ample reserves for the payouts. You purchase a card for $1 and pick any 6 numbers from 1 to 49. If your numbers match those that the state draws, you win. How many 6-number combinations are there for the drawing? If you buy one ticket, what is your probability of winning (6 out of 6)?
2007-03-20 02:39:06 · 4 answers · asked by heymyn 1 in Science & Mathematics ➔ Mathematics
# of combinations:
49x48x47x46x45x44 / (1x2x3x4x5x6) = 13,983,816
Probability of winning = 1 in 13,983,816
2007-03-20 02:44:08 · answer #1 · answered by morningfoxnorth 6 · 0⤊ 0⤋
Formula for different combinations of picking k units out of n is:
n!/(k!(n-k)!)
In this case:
49!/6!43! = 49*48*47*46*45*44/(1*2*3*4*5*6) =
=49*47*46*45*44/3*5 = 49*47*46*3*44 = 13,983,816
So over time, Michigan will be making lots of money
2007-03-20 09:46:21 · answer #2 · answered by blighmaster 3 · 0⤊ 0⤋
49c6, or the combination of 49 things taken 6 at a time.
One out of 49!/(6!*43!) = One out of (49*48*47*46*45*44)/(6*5*4*3*2*1) = 1:13,983,816.
2007-03-20 09:45:56 · answer #3 · answered by Dave 6 · 0⤊ 0⤋
13,983,816 six-number combinations.
This number comes from 49*48*47*46*45*44 all divided by
6*5*4*3*2*1.
So you have one chance in 13,983,816 of winning.
Save your dollar and buy some candy instead.
2007-03-20 09:46:41 · answer #4 · answered by mmlxxviii 2 · 0⤊ 0⤋