Question

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 1

True:
- Order matters in this scenario. (First, second, third are distinct.)
- There are 2,184 ways to select a first-place, second-place, and third-place winner. (P(14,3) = 14·13·12 = 2184.)
- The probability that all three winners are from Midland High is 0.0275. (P(5,3)/P(14,3) = 60/2184 = 5/182 ≈ 0.02747.)
- The probability that all three winners are from Cassville High is 0.0549. (P(6,3)/P(14,3) = 120/2184 = 5/91 ≈ 0.05495.)

False:
- The probability that all three winners are from Leasburg High is 0.0046. The correct value is 6/2184 = 1/364 ≈ 0.00275.