A group consists of five men and eight women. Six people are selected to attend a conference. a. In how many ways can six people be selected from this group of thirteen?

b. In how many ways can six women be selected from the eight women?

c. Find the probability that the selected group will consist of all women.

Here is their argument. given the obtuse angle x, we make a quadrilateral abcd with ∠dab = x, and ∠abc = 90◦, and ad = bc. say the perpendicular bisector to dc meets the perpendicular bisector to ab at p. then pa = pb and pc = pd. so the triangles pad and pbc have equal sides and are congruent. thus ∠pad = ∠pbc. but pab is isosceles, hence ∠pab = ∠pba. subtracting, gives x = ∠pad−∠pab = ∠pbc −∠pba = 90◦. this is a preposterous conclusion – just where is the mistake in the "proof" and why does the argument break down there?

Match the term on the left with its image or description on the right. match term definition diameter a) circle a and a line segment connecting points b and c which are on the circle. circumference b) circle a and a line segment connecting points b and c which are on the circle. radius c) a piece of the circumference of a circle secant d) two circles that share the same center. concentric circles e) the distance around a circle arc f) a segment between two points on a circle that passes through its center

I'm being volume of cylinder with 13 in. radius and 30 in height answer choices in pic