Counting Techniques

The new frozen yogurt shop down the street offers 20 flavors and 8 toppings. You can order a regular, sugar, waffle, or chocolate frozen yogurt cone. How many possible frozen yogurt cones can you order (assuming that you can only get one type of cone, one flavor of ice cream, and one topping for each yogurt cone)?

• 160

• 80

• 460

• 640

A disc jockey has to choose three songs for the last few minutes of his evening show.  If there are nine songs that he feels are appropriate for that time slot, then how many ways can he choose and arrange to play three of those nine songs?

• 84

• 504

• 9!

• 3!

A school committee of 5 is to be formed from 12 students. How many committees can be formed if Paul must be on the committee?

• 325

• 330

• 335

• 340

A lottery has 45 numbers and you must pick 6 numbers. How many different combinations are possible if your lucky numbers 11 and 42 must be on the lottery ticket?

• 123,380

• 123,390

• 123,400

• 123,410

You are making a playlist of TWICE songs with 8 songs out of their 15 singles. How many selections are there if each playlist should contain Fancy, What is Love, and Yes or Yes?

• 792

• 795

• 798

• 801

In how many different possible ways can you answer a 5-question multiple choice (with 4 choices) seatwork?

• 32

• 1024

• 20

• 625

₇P₂

• 0

• 7

• 42

• 210

₁₂C₃

• 36

• 66

• 220

• 500

A team of 17 volleyball players needs to choose three players to refill the water cooler.  How many different ways can the players be chosen?  

• 3360

• 560

• 4080

• 680

If you roll two dice, how many possible outcomes?

• 360

• 1

• 36

• 12