Counting Principle, Permutations and Combinations

Which of the following can have no repeating choices and the order affects the amount of possible outcomes?

• Combination

• Permutation

• That multiplication thing...

• I don't know. Ask someone else!

In permutations and combinations, what does the n represent in nPr and nCr?

• Total number of people/things you can pick from

• Number of spots you have to fill

• N is for narwhal

• Nothing! N means nothing to me! And I'm not being dramatic!

In permutations and combinations, what does the r represent in nPr and nCr?

• Total number of choices you can make

• Number of choices that can be made

• R is for rhino

• That's what pirates say

5 different roads from city A to city B and 5 different roads from city B to city C. In how many ways can someone go from city A to city C passing by city B?

• 5

• 10

• 25

• 55

Find the number of possibilities:
A group of 25 people are going to run a race.  The top 8 finishers advance to finals.

Ambry must submit 4 paintings as part of her
application to art school. If she has 25 to choose from, how many ways can she pick 4?

• 12,650

• 303,600

• 100

• 254

Find the number of possibilities:
A team of 17 softball players needs to choose three players to refill the water cooler.

• 272

• 4080

• 680

What is C(9,4)?

• 36

• 126

• 3024

• 362880

The company Sea Esta has ten members on its board of directors. In how many different ways can it elect a president, vice-president, secretary and treasurer?

• 40

• 210

• 5040

• 3628800

To win the small county lottery, one must correctly select 3 numbers from 30 numbers. The order in which the selection is made does not matter. How many different selections are possible?

• 30!

• 90

• 4060

• 24360