Set cap x is made up of the possible ways five students, represented by cap A , cap b , cap c , cap d , and cap e , can be formed into groups of three. Set cap y is made up of the possible ways five students can be formed into groups of three if student cap A must be in all possible groups. Which statements about the situation are true? Choose three correct answers.

A group in set Y must contain A, so the other two students are chosen from B, C, D, and E. This gives ABC, ABD, ABE, ACD, ACE, and ADE, making statement A true. If A and C are both required, the third student can be B, D, or E, so there are three groups and statement D is true. Set X has 5 choose 3 = (5 × 4 × 3) ÷ (3 × 2 × 1) = 10 groups, so statement E is true. Y is a strict subset of X, and requiring E still allows six groups, so B and C are false.

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