Alocal chess tournament gives medals for first, second, and third place. there are five students from midland high, three students from leasburg high, and six students from cassville high competing in the tournament. which statements are true? check all that apply. order matters in this scenario. there are 2,184 ways to select a first-place, second-place, and third-place winner. the probability that all three winners are from midland high is 0.0275. the probability that all three winners are from leasburg high is 0.0046. the probability that all three winners are from cassville high is 0.0549

The correct answers are:

There are 2,184 ways to choose a first, second and third place winner.
The probability that all 3 winners are from Midland High is 0.0275.
The probability that all 3 winners are from Cassville High is 0.0549.

Explanation:

There are 5+3+6=14 total students competing.

This means to find the total number of first, second and third place winners, we take a permutation of 14 objects taken 3 at a time:



To find the probability that all 3 winners are from Midland High, we first find the number of ways that 3 winners can be chosen from Midland High.  This is a permutation of 5 objects taken 3 at a time:



There are 60 possible ways to select the winners from Midland High.  This is out of 2184 total ways, so the probability is:
60/2184 = 0.0275

To find the probability that all 3 winners are from Leasburg High, we first find the total number of ways to select 3 winners from Leasburg High.  This is a permutation of 3 objects taken 3 at a time:



There are 6 possible ways to select 3 winners from Leasburg High.  This is out of a total of 2184 ways to select the winners; this makes the probability 
6/2184 = 0.0028.  This is not one of our options.

To find the probability of selecting all 3 winners from Cassville High, we first find the total number of ways of selecting 3 winners from Cassville High.  This is a permutation of 6 objects taken 3 at a time:



There are 120 ways to select 3 winners from Cassville High.  This is out of a total number of 2184 ways to select 3 winners; this makes the probability 
120/2184 = 0.0549.