Question

In a certain​ lottery, an urn contains balls numbered 1 to 34. 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? g

Answer 1

$\displaystyle |\Omega|=\binom{34}{6}=\dfrac{34!}{6!28!}=\dfrac{29\cdot30\cdot31\cdot32\cdot33\cdot34}{2\cdot3\cdot4\cdot5\cdot6}=1344904\\ |A|=1\\\\ P(A)=\dfrac{1}{1344904}$