∆ABC has vertices at A(11, 6), B(5, 6), and C(5, 17).
∆XYZ has vertices at X(-10, 5), Y(-12, -2), and Z(-4, 15).
∆MNO has vertices at M(-9, -4), N(-3, -4), and O(-3, -15).
∆JKL has vertices at J(17, -2), K(12, -2), and L(12, 7).
∆PQR has vertices at P(12, 3), Q(12, -2), and R(3, -2).

can be shown to be congruent by a sequence of reflections and translations. can be shown to be congruent by a single rotation.

Out of five men and five women, we form a committee consisting of four different people. assuming that each committee of size four is equally likely, find the probabilities of the following events: 1. the committee consists of two men and two women 2. the committee has more women than men. 3. the committee has at least one man. for the remainder of the problem assume that alice and bob are among the ten people being considered. 4. both alice and bob are members of the committee.