Five cards are drawn at random from a 52card deck a Compute

Five cards are drawn at random from a 52-card deck.
(a). Compute the probability that at least two of them are spades.
(b). What is the probability that it will be a straight (Five cards in a sequence, regardless
of suit. For example, 3,4,5,6,7 or 9,10, J, Q, K. Be careful that A can either be the mini-
mum or the maximum).

Solution

A)

There are 52C5 ways to draw any 5 cards.

There are 13C2 ways to get 2 spades, and then 50C3 ways to get any other three.

Thus,

P = ([13C2][50C3])/(52C5) = 0.588235294 [ANSWER]

*****************

B)

There if the starting rank is fixed, there are 4*4*4*4*4 = 1024 ways to get a straight. However, there are 10 different starting ranks available, so there are 1024*10 = 10240 straights.

Thus,

P(straight) = 10240 / 52C5 = 0.003940038 [ANSWER]