(a) You spend an evening at the movies with Pat (your significant other) and fou
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Question
(a) You spend an evening at the movies with Pat (your significant other) and four other friends of yours. If all six of you sit next to each other, but in a completely random order, evaluate the following: (i) What is the probability that you and Pat end up in the two seats on the far left? (ii) What is the probability that the two of you sit next to each other at all? (b) In five-card poker, a flush consists of five cards of the same suit; a straight consists of five cards of consecutive denominations (e.g., 2, 3, 4, 5, and 6) (aces can be high or low, and suit doesn't matter); and a straight flush is a hand which is both a straight and a flush (five consecutive cards of the same suit). Assuming a hand of five cards dealt from a standard 52-card deck, what is the probability of being dealt (i) a flush, ) a straight,, and (iii) a straight flush?Explanation / Answer
a) Total no. of ways = 6!
No. of arrangements with Pat and I togther on the far left = 4!
Now, Pat and I can exchange seats in two ways.
Probabiliy = 2*4!/6! = 1/15
b) P( always next to each other) = 2* 5!/6! = 1/3
p( Never next to each othr ) = 1-1/3=2/3
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