A ﬂush in the card game of poker occurs if a player gets ﬁve cards that are all the same suit (clubs, diamonds, hearts, or spades). Answer the following questions to obtain the probability of being dealt a ﬂush in ﬁve cards.
(a) We initially concentrate on one suit, say clubs. There are 13 clubs in a deck. Compute P(five clubs) = P(ﬁrst card is clubs and second card is clubs and third card is clubs and fourth card is clubs and ﬁfth card is clubs).
(b) A ﬂush can occur if we get ﬁve clubs or ﬁve diamonds or ﬁve hearts or ﬁve spades. Compute P(ﬁve clubs or ﬁve diamonds or ﬁve hearts or ﬁve spades). Note that the events
are mutually exclusive.