Quote:
Originally Posted by Velvet
A music festival award gives awards for 1st, 2nd and 3rd place in each category. If there are 7 contestants for piano and 9 for violin, in how many different ways could the 6 awards be presented?
|
For the piano (7 total participants): There are 210 possible arrangements (permutations) of 3 participants. 7 possibilities for 1st Place, 6 possibilities for 2nd place, and 5 possibilities for 3rd place. Multiplying these (7x6x5) gives you 210 possible arrangements.
For the Violin (9 total participants) : There are 504 possible arrangements (permutations) of 3 participants. 9 possibilities for 1st Place, 8 possibilities for 2nd place, and 7 possibilities for 3rd place. Multiplying these (9x8x7) gives you 504 possible arrangements.
So, the total number of ways the trophies can be presented is 7 x 6 x 5 x 9 x 8 x 7 = 105,840.
[ In other words the piano 1st place trophy would be given to one of seven participants; the piano 2nd place trophy would be given to one of the remaining six participants, and the piano 3rd place trophy would be given to one of the remaining 5 participants. Similarly, the violin 1st place trophy would be given to one of nine participants; the violin 2nd place trophy would be given to one of the remaining eight participants; and the violin 3rd place trophy would be given to one of the remaining 7 participants. ]