How many ways can first, second, and third place be assigned?At a gymnastics meet, twenty gymnasts compete for first, second, and third place.

Answer:The total number of ways can first, second and third place can be assigned are:                           6840Step-by-step explanation:The total number of people that compete are: 20Out of these 20 people we have to chose 3 people and also arrange them according to their ranks.We know that when we have to choose and  arrange r items out of total n items then we need to use the method of permutation.Hence, the formula is given by:[tex]n_P_r=\dfrac{n!}{(n-r)!}[/tex]Here we have:n=20 and r=3Hence, the number of ways first, second and third place can be assigned are:[tex]{20}_P_3=\dfrac{20!}{(20-3)!}\\\\\\{20}_P_3=\dfrac{20!}{17!}\\\\\\{20}_P_3=\dfrac{20\times 19\times 18\times 17!}{17!}\\\\\\{20}_P_3=20\times 19\times 18\\\\\\{20}_P_3=6840[/tex]          Hence, the answer is:                  6840