Thread: Story Problem for 4th Grade Homework

Eight runners are entered in the 1000-meter run. How many different first, second, and third place finishes could possibly occur? I have no idea how to start to help my daughter with this problem. Thanks for any help you can give this math-challenged mom.

Hi gitai

Number of persons that can be the first = 8
Number of persons that can be the second = 7 (because 1 person has finished first)
Number of persons that can be the third = ....

Have any ideas to continue?

we found a combinations/permutations calculator on-line, so we said:
Types to Choose (meaning how many runners): 8 = n
Number Chosen (meaning first place, second place and third): 3 = r

and repetition is not allowed meaning we used this formula:

n!/(n-r)! = 8!/(8-3)!

Now of course we needed to find out that ! is a factorial

8! = 8x7x6x5x4x3x2x1 or 40,230
(8-3) = 5! = 5x4x3x2x1 or 120

40,230/120 = 336 possible combinations

Are we correct?

Hi gitai

Absolutely correct

Thank you Songoku! We are very proud of ourselves!

Or if you want a more basic solution>

Possible number of first place = 8
Second place = 7
Third place = 6

(as songoku said)

Therefore, possible combinations = 8 * 7 * 6 = 336