Question

There are fifteen people competing in an event. How many ways are there for people to finish first, second, and third?

Answer 1

15*14*13

An example is:
In a race of 7 women, in how many ways can first, second, and third place ribbons be awarded?
From the 7 women there are 7 possible winners, and then 6 possible runner-ups, and finally 5 possible third place finishers. We are choosing 3 from 7 and placing them in an order; the number of ways is

P(7,3) = 7 · 6 · 5 = 210 .

Answer 2

so 15*14*13 is 2730

Answer 3

can you help me with another @cheyenne8 The game of euchre uses only 24 cards from a standard deck. How many different 5 card euchre
hands are possible?

Answer 4

" The number of permutations is 24 * 23 * 22 * 21 * 20 = 5,100,480 but we don't care about the order of the cards, so we have to account for that.
The number of combinations is 24 * 23 * 22 * 21 *20/(5 * 4 * 3 * 2 * 1)
The first card can be any of the 24, the second, any of the remaining 23, and so on until we have 5 cards. This is where our numerator comes from.
The first of the 5 cards can be any of the 5, the second can be any of the 4, and so on. This is where our denominator comes from. "

The formula would be C(24,5) = 24!/((24-5)!*5!) , using factorials and the answer would be 42,504 possible hands