I need help solving this permulation...10 students are running a race. The fastest 3 will win a gold, silver, or bronze medal. How many different ways can the students win these medals?

Question

anonymous · Answer

its been a while since ive done this type of question but if you have a graphing calculator, it has a feature that will do permutations for you

anonymous · Answer

i left mine at my friends but i do have one. what do i plug in? what equation?

anonymous · Answer

I suggest that you check with a friend but go if you have a TI-84 like me, then go to the math section and pick npr, I got the answer of 720 because order doesn't matter

anonymous · Answer

if its a combination question then the answer would be 120

anonymous · Answer

ok  that sounds good. so for permutations the order doesnt matter but combinations it does right?

anonymous · Answer

I was wrong, for permutations the order does matter and the order does not matter for combinations, so the answer would be 120 I believe

anonymous · Answer

what would be the equation you used to get that?

anonymous · Answer

I'm pretty sure that there is an equation for it, which you can find if you search it up, but I primarily use my calculator and input 10 - math - nCr - 3 to get this answer, its much faster

kropot72 · Answer

The order in which the 3 fastest students finish is important. There are 6 ways of arranging the fastest 3 into 1st, 2nd and 3rd place. Therefore the formula for permutations must be used. The number of permutations of n different things taken r at a time is
$$nPr=\frac{n!}{(n-r)!}=\frac{10!}{(10-3)!}=10\times 9\times 8=?$$