a local chess tournament gives medals for first, second, and third place. there are five students from…

a local 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

a local 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

Answer

Explanation:

Step1: Determine if order matters

Since there are first, second, and third - place medals, order of selection matters.

Step2: Calculate total number of students

There are (5 + 3+6=14) students. The number of ways to select 3 students for first, second, and third place (using permutations (P(n,r)=\frac{n!}{(n - r)!}), where (n = 14) and (r=3)) is (P(14,3)=\frac{14!}{(14 - 3)!}=\frac{14!}{11!}=14\times13\times12 = 2184).

Step3: Calculate probabilities for each school

  • Probability that all three winners are from Midland High: The number of ways to select 3 students from 5 students of Midland High for first, second, and third place is (P(5,3)=\frac{5!}{(5 - 3)!}=\frac{5!}{2!}=5\times4\times3 = 60). The probability is (\frac{P(5,3)}{P(14,3)}=\frac{60}{2184}\approx0.0275).
  • Probability that all three winners are from Leasburg High: The number of ways to select 3 students from 3 students of Leasburg High for first, second, and third place is (P(3,3)=\frac{3!}{(3 - 3)!}=3! = 6). The probability is (\frac{P(3,3)}{P(14,3)}=\frac{6}{2184}\approx0.0027\neq0.0046).
  • Probability that all three winners are from Cassville High: The number of ways to select 3 students from 6 students of Cassville High for first, second, and third place is (P(6,3)=\frac{6!}{(6 - 3)!}=\frac{6!}{3!}=6\times5\times4 = 120). The probability is (\frac{P(6,3)}{P(14,3)}=\frac{120}{2184}\approx0.0549).

Answer:

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 Cassville High is 0.0549.