Suppose there are eight socks in a bag which can be grouped into four pairs: {BR1, BR2}, {BG1, BG2}, {GR1, GR2}, or {GG1, GG2}. The socks of each pair have the same color (Red or Green) and are gender specific (Boy or Girl), e.g., BR1 is a red colored boy's socks. Suppose there are two boys and two girls present, and one at a time in a fixed order, they each draw two socks out of the bag, without replacement. Suppose all socks feel the same, so when two socks are drawn from the bag, all possibilities have equal probability. Let M be the event that each person draws a pair of socks that match in color and their gender. (a) Define a sample space for this experiment. Suppose that the order that the people draw the socks doesn't matter-all that is recorded is which two socks each person selects. (b) Determine |22|, the cardinality of . (c) Determine the number of outcomes in M. (d) Find P(M). (e) Find a short way to calculate P(M) that does't require finding |M| and ||. (Hint: Write P(M) as one over an integer and factor the integer and think about the probability of each step of the drawing procedure.)