Answer
Probability that the person with one ticket will win the lottery = $\frac{1}{18009460}$
Probability that the person with 100 different tickets will win the lottery = $\frac{5}{900473}$
Work Step by Step
There is only one way of winning, Thus the number of favorable outcomes = 1
The sample space is the set of all possible six number combinations.
We can use the combinations formula $n_{C}{_{r}}$ = $\frac{n!}{(n - r)! r!}$ to find the total number of possible combinations.
We are selecting r =6 numbers from a collection of n = 51 numbers.
$51_{{C}{_{6}}}$ = $\frac{51!}{(51 - 6)! 6!}$
= $\frac{51!}{45!.6!}$ = $\frac{51\times50\times49\times48\times47\times46\times45!}{45! .6\times5\times4\times3\times2\times1}$
= 18009460
Thus total number of outcomes = 18009460
The number of favorable outcomes = 1
Probability = $\frac{Numberof favorable outcomes}{Total outcomes}$
Probability that the person with one ticket will win the lottery = $\frac{1}{18009460}$
Probability that the person with 100 different tickets will win the lottery = $\frac{100}{18009460}$ = $\frac{5}{900473}$
