Question

In a certain​ lottery, an urn contains balls numbered 1 to 26. From this​ urn, 6 balls are chosen​ randomly, without replacement. For a​ $1 bet, a player chooses one set of six numbers. To​ win, all six 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

\frac{1}{230230}

Explanation:

Given that in a certain​ lottery, an urn contains balls numbered 1 to 26

From this​ urn, 6 balls are chosen​ randomly, without replacement.

Bet amount 1 dollar and he selects a set of six numbers.

If these match with those chosen from the urn he wins (order does not matter)

Total ways of choosing 6 out of 26 =
`26C6 = (26!)/(20!6!) \\=230230`

The way he selects = 1

Hence probability of winning =
`(1)/(230230)`

with one ticket