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Let the helmets which Gary, Yuri and Cris had checked in previously be denoted as G, Y and C. As the helmets are received in the order of Gary, Yuri and Cris, there is a match if each of them gets their own helmet. As there are 3 helmets, the total number of possible orders are 3! = 6. These are listed below
If the first helmet returned is G, then it's a match for Gary. If the second helmet returned is Y, then it's a match for Yuri, and if the third helmet returned is C, then it's a match for Cris. Using this reasoning, the number of correct matches denoted by the variable X is as shown in the below table