In how many ways can president, vice-president, and secretary be chosen from a group of 20 people, if Sarah, one of the 20 people, does not want to be president, but is willing to hold either of the other positions?

please very soon answer both parts Question 2 a. A company plans to interview ten recent graduates for possible employment. The company has three positions open. How many groups of three can the company select if the order of arrangement is not important? b. A student has to take nine more courses before he can graduate. If some of the courses are prerequisite to others and therefore the order of arrangement is important, in how many ways can the student arrange four courses for the next semester?

A particular American football play has eleven players: one quarterback, one running back, one center, two wide receivers, and six more offensive players. The coach calling the play has 3 quarterbacks, 2 running backs, 1 center, 4 wide receivers, and 20 other offensive players to choose from. When the play is called, the participating eleven players go onto the field to join the huddle in any order. Then, the play is lined up, where the participating players arrange themselves on the field in a particular way. (a) How many different possible combinations of players could there be in the huddle before the play is lined up? (b) When the particular play is lined up, the offensive line is in the center of the field with three offensive players on each side of the center player (seven players total). The two wide receivers line up on opposite sides of the offensive line - one on the left, and one on the right. The quarterback is lined up behind the center, and the running back is lined up…

A clothing store has a certain shirt in 4 sizes: small, medium, large, and extra-large. If it has 2 small, 3 medium, 6 large, and 2 extra-large in stock, How many orders can it sell all the shirts? Suppose the store decides not to sell the extra-large shirts. In how many orders can it sell the remaining shirts?

In a linguistics program there are 61 students.  Of these students, 30 of the students speak Finnish, 24 speak German, 23 speak Italian. We know that 17 speak Finnish and German, 14 speak Finnish and Italian, and 12 speak German and Italian. If 19 speak none of these three languages, then how many speak all three languages?

1) There are 18 offensive players on the hockey team. How many ways can the coach choose a left wing, center, and right wing to start the game?

Consider the following problem: Three officers-a president, a treasurer, and a secretary-are to be chosen from among four people: Ann, Bob, Cyd, and Dan. Suppose that, for various reasons, Ann cannot be president and either Cyd or Dan must be secretary. How many ways can the officers be chosen?

Suppose there are 14 freshman, 13 sophomores, 15 juniors, and 17 seniors running for the offices of president, vice president, and secretary. If no person can hold more than one office, in how many different ways could these people be elected to these positions?

A camp counselor and eight campers are to be seated along a picnic bench. In how many ways can this be done if the counselor must be seated in the seventh seat and a camper who has a tendency to engage in food fights must sit to the counselor's immediate right?

In a survey of 252 professional athletes, it was found that 119 of them owned a convertible, 122 of them owned a giant screen TV, and 115 owned a sporting goods store. 21 owned a convertible and a store, 44 owned a TV and a store, and 73 owned a covertible and a TV. 13 owned all three items. How many athletes did not own any of the three items? How many owned a covertible and a TV, but not a store? How many athletes owned a convertible or a TV? How many athletes owned exactly one type of item in the survey? How many athletes owned at least one type of item in the survey? How many owned a TV or a store, but not a convertible?