The total number of ways can first, second and third place can be assigned are:
6840
The total number of people that compete are: 20
Out 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=3
Hence, 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
Answer:
The correct answer is
1. 6,840
2. 342
3. 18
At a gymnastics meet, twenty gymnasts compete for first, second, and third place.
