1 Suppose n objects are permuted at random among themselves

1) Suppose n objects are permuted at random among themselves, what is the probability that k specified objects occupy k specified objects? (Each of k specified objects occupies a specified position)

2) There are two boxes, each has 10 balls numbered 1 through 10. A random sample of 6 balls is drawn, without replacement, from each box. Find the probability that the samples contain exactly 3 balls having the same numbers in common.

3) Let A1, A2, A3 be (mutually) independent events and P(Ai) = 0.i, i = 1, 2, 3. Find the probability that at least one Ai occurs.

Solution