Math Problem of the Week - Algebra and Up - June 6, 2021 to June 12, 2021

Algebra and Up: 

Question: In the game Clue, there are 6 suspect cards, 6 tool cards, and 9 location cards. A combination of 1 suspect, 1 tool, and 1 location is selected at random at the beginning of the game and put in an envelope. What is the probability that the combination in the envelope is the Candlestick, the Library, and anyone but Colonel Mustard? 

Answer:   ⁵/₃₂₄

Solution:  The probability that the crime took place in the Library with the Candlestick is ¹/₉ × ¹/₆ = ¹/₅₄. There are 5 suspects who aren’t Colonel Mustard, so that means that the probability that anybody but Colonel Mustard committed the crime in the Library with the Candlestick is ¹/₅₄ × ⁵/₆ = ⁵/₃₂₄.