The math club at college has 16 students - 10 males and 6 females. (a) The club wants to select a group of 4 students to take part in a math competition. In how many ways can they do it if at least two females are chosen? (give a nurmerical answer) (b) The club wants to elect a president, a vice president, a treasurer and a secretary for the class. In how many ways can they do that? (c) A local company has donated 32 identical pens to be distributed to the club members. In how many ways can they be distributed so that each student gets at least one pen, and the secretary of the club gets at least 4.

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.

A math instructor has 35 calculators in her office. Of them, 17 have dead batteries, 13 have cracked displays, and 22 have missing buttons. Of those with dead batteries, 5 have cracked displays and 11 have missing buttons. Of those with cracked displays, 8 have missing buttons. There are 3 with dead batteries, cracked displays, and missing buttons. How many calculators does she have with nothing wrong with them? (A) 4 (B) 6 (C) 3 (D) 7 (E) 8 (F) 2 (G) 1 (H) 9 O A OB OC OD OE OF H.

At the National Baseball Batting Contest, the organizers have set up game booths for the contestants. Richard wants to win a large stuffed animal. The rules of the game are as follows: You are pitched 5 fastballs, and you must hit them into a fair zone to count. • If you successfully hit all 5 pitches, you win a large stuffed animal. If you successfully hit 3 or 4 pitches, you win a small stuffed animal. • If you successfully hit 1 or 2 pitches, you win a bat-shaped pencil. If you miss all the pitches, you do not win a prize. • The game costs $3 to play (each set of 5 fastballs). Everyone has the same chance as Richard to win. If 160 people each play the game once, how many large stuffed animals will be won?

A survey of 1900 commuters in New York City showed that 1180 take the subway, 650 take the bus, and 170 do not take either the bus or the subway. (a) How many commuters take both the bus and the subway?(b) How many commuters take only the subway?

Jessica is grocery shopping and has 16 cherry tomatoes and 12 grape tomatoes in her shopping basket. When she gets home, she prepares her ingredients for lunch, but she forgets which of the tomatoes are cherry and which are grape. She cannot distinguish between the two types of tomatoes, so she just picks 13 tomatoes. How many different sets of 13 tomatoes are possible if there are exactly 7 cherry tomatoes?

A math instructor has 46 calculators in her office. Of them, 22 have dead batteries, 28 have cracked displays, and 24 have missing buttons. Of those with dead batteries, 16 have cracked displays and 11 have missing buttons. Of those with cracked displays, 18 have missing buttons. There are 9 with dead batteries, cracked displays, and missing buttons. How many calculators does she have with nothing wrong with them? (A) 6 (В) 4 (C) 5 (D) 9 (E) 8 (F) 3 (G) 1 (H)

I just need help solving this.

54 people are competing in an athletic event. The top 4 competitors receive prize money, with 1st being worth more than 2nd,2nd worth more than 3rd, etc. How any ways can the 4 prizes be given?

At the World Goldendoodle Championship, 16 doodles compete to see who is the fluffiest.  The top five contests receive prizes and cash: 1st = $300,000 2nd = $100,000 3rd = $50,000 4th = $25,000 5th = $10,000 Obviously, being first is better than being fifth.  How many ways can the 16 doodles make the top five?