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Montano1993 [528]
3 years ago
15

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

ce be assigned? Third place has been announced. In how many ways can the remaining two places be assigned? Third and second places have been announced. In how many ways can first place be assigned?
Mathematics
2 answers:
ExtremeBDS [4]3 years ago
7 0
Part A:

Given that a<span>t a gymnastics meet, twenty gymnasts compete for first, second, and third place. The number of ways </span><span>first, second, and third place can be assigned</span><span> is given by

^{20}P_3= \frac{20!}{(20-3)!}  \\  \\ = \frac{20!}{17!} =20\times19\times18 \\  \\ =6,840\ ways



Part B:

</span>Given that at a gymnastics meet, twenty gymnasts compete for first, second, and third place. If the t<span>hird place has been announced the number of ways that the remaining two places can be assigned</span> is given by :

<span>^{19}P_2= \frac{19!}{(19-2)!}  \\  \\ = \frac{19!}{17!} =19\times18 \\  \\ =342\ ways
</span>


Part C:

Given that at a gymnastics meet, twenty gymnasts compete for first, second, and third place. If the third and second places have been announced the number of ways that the <span>first place</span> can be assigned is given by :

^{18}P_1= \frac{18!}{(18-1)!}  \\  \\ = \frac{18!}{17!} =18\ ways
mojhsa [17]3 years ago
7 0

The correct answer is:

1. 6,840

2. 342

3. 18

At a gymnastics meet, twenty gymnasts compete for first, second, and third place.

|Huntrw6|

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