Question

In a certain​ lottery, an urn contains balls numbered 1 to 37. From this​ urn, 4 balls are chosen​ randomly, without replacement. For a​ $1 bet, a player chooses one set of four numbers. To​ win, all four numbers must match those chosen from the urn. The order in which the balls are selected does not matter. What is the probability of winning this lottery with one​ ticket?

Answer 1

Number of ways 4 balls are chosen​ randomly, without replacement (when order in which the balls are selected does not matter)  = ³⁷C₄

= 37! / [(37 - 4)! * 4!]

= 37! / (33! * 4!)

= (37 * 36 * 35 * 34) / (4 * 3 * 2 * 1)

= 66045

For a​ $1 bet, a player can choose only one set of four numbers out of 66045 sets.

So, the probability of winning this lottery with one​ ticket = 1 / 66045