Tim K. answered • 06/08/20
Expert STEM Tutor with 12+ Years of Tutoring & Teaching Experience
The probability of winning is equal to the number of winning combinations divided by the total number of possible lottery combinations. The total number of possible lottery combinations is expressed as
( n r ) = n! / [r! * (n-r)!]
A 5/43 lottery thus has 43!/[5!*38!] combinations, or 962,598.
There is only one first place combination (all five numbers match). There are five second place combinations (four numbers match, one does not). Thus the number of first and second place winning combinations is six, and the probability of a first or second place winning combination in a 5/43 lottery is
6/962598 = 1/160433 or about 0.000623%
