Question

Calculate each of the following events
(1) A box of 50 light bulbs contains 3 defectives. If 5 bulbs are sampled at random from this box (without replacement), find the probability that the sample contains no defectives

(2) A drawer of socks contains seven identical red socks, eight identical blue socks and nine identical green socks. Two socks are randomly picked out in the dark. What is the probability that they match?
(3) Thirty people are gathered in a room. What is the probability that at least two of them have the same birthday? (Assume that each person’s birthday is equally likely to fall on any day of the year, and ignore leap years.)
(4) How many ways can 11 boys on a soccer team be grouped into 4 forwards, 3 midfielders, 3 defenders, and 1 goalie?

Answer 1