Question

Set X is made up of the possible ways five students, represented by A, B, C, D, and E, can be formed into groups of three. Set Y is made up of the possible ways five students can be formed into groups of three if student A must be in all possible groups.

Which statements about the situation are true? Select three options.

Set X has 10 possible groupings.
X Y
Set Y = {ABC, ABD, ABE, ACD, ACE, ADE}
If person E must be in each group, then there can be only one group.
There are three ways to form a group if persons A and C must be in it.

Answer 1

The true statements are:

- Set X has 10 possible groupings. (C(5,3) = 10.)
- Set Y = {ABC, ABD, ABE, ACD, ACE, ADE}. (All 3-person groups that include A: C(4,2)=6.)
- There are three ways to form a group if persons A and C must be in it. (With A and C fixed the third member can be B, D, or E.)

The other two are false: if E must be in each group there are C(4,2)=6 groups (not 1), and the remaining relation shown between X and Y as printed is not one of the three true choices above.