Respuesta :
For use to be able to determine how many ways can first, second, and third place be awarded to 3 contestants, we will be using the permutation formula.
[tex]\text{ nPr = }\frac{n!}{(n\text{ - r)!}}[/tex]Where,
P = the number of permutations
n = total number of objects in the set = 3 contestants = 3
r = number of choosing objects from the set = 1st, 2nd & 3rd place = 3
We get,
[tex]\text{ nPr = }\frac{n!}{(n\text{ - r)!}}[/tex][tex]\text{ }_3P_3\text{ = }\frac{3!}{(3-3)!}[/tex][tex]\text{= }\frac{3\text{!}}{0!}\text{ = }\frac{\text{ 3 x 2 x 1}}{1}[/tex][tex]\text{ = }\frac{\text{6}}{1}\text{ = 6}[/tex]Therefore, there are 6 possible ways can first, second and third place be awarded to 3 contestants.
The answer is 6.
