How many six-person lineups can be formed from a 10-player volleyball roster? (Every player plays every position)

How many 5-card hands can be chosen from a deck of cards?

Assume that there are 4 types of upholstery, 4 types of wood, and 5 designs to choose from. Of the designs, 4 designs permit both a choice of wood and a choice of upholstery, but 1 of the design allows only a choice of upholstery. How many different chairs can be made?

A group of 13 people consisting of 3 freshmen, 2 sophomores, 4 juniors, and 4 seniors are selected from 6 freshmen, 5 sophomores, 5 juniors, and 7 seniors. How many groups can be formed?

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?

How many 5 card hands possible with a 26 card deck?

There are 10 trivia teams (Teams A through J), each with 5 members. 16 areselected for an all-star team. How many ways are there to select an all-star team which includes all members from A, all members from B, all members from C, or all members from D?

In a club with 10 male and 11 female members, how many 6-member committees can be selected that have not more than 2 men?

A bag contains three red marbles, six green ones, one lavender one, two yellows, and three orange marbles. How many sets of three marbles include all the yellow ones? sets