There are 8 winning tickets in the lottery of 40 tickets. What is the probability that among

There are 8 winning tickets in the lottery of 40 tickets. What is the probability that among the first five randomly selected tickets, two will be won?

The total number of ways to take out five tickets out of forty:
C (40.5) = 40! / (5! (40 – 5)!) = 36 37 38 39 40 / (1 2 3 4 5) = 658008;
The number of ways to get two winning tickets out of 8 are:
C (8.2) = 8! / (2! (8 – 2)!) = 7 8 / (1 2) = 28;
The number of ways to get three tickets without winning out of the 32 remaining:
C (32.3) = 32! / (3! (32 – 3)!) = 30 31 32 / (1 2 3) = 4960;
The probability that among the first five tickets chosen at random, two will be winning:
P5 (2) = C (8.2) C (32.3) / C (40.5) = 28 4960/658008 = 0.211;
Answer: 0.211.