5 women and 4 women compete in separate bike races In both r

5 women and 4 women compete in separate bike races. In both races, a gold medal is given to the winner, and a silver medal to the runner-up. In how many different ways can the medals be assigned?

A hat contains 4 slips of paper numbered 1 through 4. An experiment consists of drawing two slips of paper from the hat without replacement. Find the probability that two numbers drawn will add up to 5 or more.

Solution

There are 9 people, and you can distinguish them.

Order matters as this affects rank.

thus, there are 9P2 = 72 ways to do this. [ANSWER]

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There are 4P2 = 12 ways to draw 2 slips.
Of these 12, these add up to 5 or more:

1,4
2,3
2,4
3,2
3,4
4,1
4,2
4,3 [8 results]

hence,

P(5 or more) = 8/12 = 2/3 = 0.666667 [ANSWER]