A group contains n men and n women. How many ways are there to arrange these people in a row if the men and women alternate?

A group of 11 people consisting of 2 freshmen, 1 sophomores, 4 juniors, and 4 seniors are selected from 4 freshmen, 5 sophomores, 5 juniors, and 7 seniors. How many groups can be formed?

Suppose there are 6 girls and 6 boys in a class. In how many ways can you arrange these children in a row if two of the girts are frends and mut st ret ah other?

A teacher will randomly award three students with extra credit. How many possible ways can the teacher pick these three students from a class of 20 students?

A legislative committee consists of 4 Democrats and 9 Republicans. A delegation of 4 is to be selected to visit a small island republic. Complete parts (a) through (d) below. (a) How many different delegations are possible? The 4 delegates can be selected different ways. (b) How many delegations would have all Democrats? The 4 delegates can be selected different ways if all 4 are Democrats (c) How many delegations would have 3 Democrats and 1 Republican? The 4 delegates can be selected different ways if 3 are Democrats and 1 is a Republican (d) How many delegations would include at least 1 Republican? The 4 delegates can be selected different ways if at least 1 is a Republican,

A basket contains 2 pink, 3 yellow, 8 red, and 1 black jelly beans. You grab a handful of 4 jelly beans. (a) How many groups of 4 jelly beans include exactly 1 of each color?   (b) How many groups of 4 jelly beans include at most 1 yellow?

At the beginning of a game of chess, the back row consists of two (identical) rooks on the corners, then two knights next to them, then two bishops, and finally a king and a queen in the center. Bobby Fischer, an American chess legend, popularized the idea of randomly shuffled starting positions. Inhow many distinct ways can the eight pieces above be aligned?