(a) How many trucks carried only late variety peaches? 18 trucks (Type a whole number.) (b) How many carried only extra late? 17 trucks (Type a whole number.) (c) How many carried only one type of peach? trucks (Type a whole number.)

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A pizza parlor offers 14 toppings. a. How many 4-topping pizzas could they put on their menu? Assume double toppings are not allowed. b. How many total pizzas are possible, with between zero and 14 toppings (but not double toppings) allowed? c. The pizza parlor will list the 14 toppings in two equal-sized columns on their menu. How many ways can they arrange the toppings in the left column?

A large research project is looking for more researchers. There are 8 spots open on the research team. There are 10 mathematicians and 14 computer scientists that apply for the team. a. How many different ways can a team of 8 be made for the project? b. How many different ways can a team of 8 be made for the project if the team must contain at least one computer scientist and at least one mathematician.

From a standard 52-card deck, how many 9-card hands consist of 5 diamonds and 4 clubs? ​

A class has 32 students. In how many different ways can six students form a group for an activity? (Assume the order of the students is not important.) There are different ways that the six students can form a group for an activity. (Type a whole number.)

(a) In how many ways can 4 boys and 3 girls sit in a row. (b) In how many ways can they sit in a row if the boys and girls dare each to sit together

In how many ways can 10 engineers and 4 doctors be seated at a round table if no two doctors sit together? * 9! x 10P4 10! x 10P4 10! x 4! O 13!

There are 45 runners in a race. How many ways can the runners finish first, second, and third? There are different ways that the runners can finish first through third. (Type a whole number.)

Q. 3 professors and 3 students are sit in a row (i) How many seating arrangements are there?, (ii) How many seating arrangements if the professors sit just together and students sit just together. (iii) How many seating arrangements are there if the professors and the students sit together? (iv) How many seating arrangements are there if the professors and the students must alternate? (v) How many seating arrangements are there if only the professors must sit together?