Exploring Combinations and Permutations

What is the formula for calculating permutations of n items taken r at a time?

• P(n, r) = n! + (n - r)!

• C(n, r) = n! / (r! (n - r)! )

• P(n, r) = n! * r!

• P(n, r) = n! / (n - r)!

How many ways can you arrange the letters in the word 'MATH'?

• 36

• 18

• 24

• 12

If you have 5 different books, how many ways can you choose 3 to read?

• 15

• 10

• 20

• 5

What is the difference between combinations and permutations?

• Permutations can only be used with distinct items.

• Combinations are always larger than permutations.

• Combinations do not consider order; permutations do.

• Combinations require all items to be selected.

Calculate the number of ways to select 2 fruits from a basket of 5 different fruits.

• 15

• 20

• 10

• 5

In how many ways can 4 people be seated in a row?

• 30

• 12

• 24

• 16

If a committee of 3 is to be formed from 10 people, how many different committees can be formed?

• 120

• 45

• 30

• 60

What is the number of ways to arrange the letters in the word 'LEVEL'?

• 25

• 30

• 40

• 15

If you roll a die, what is the probability of getting a 3 or a 4?

• 1/3

• 1/4

• 1/2

• 2/3

How many different ways can you select 4 toppings from a choice of 10 for a pizza?

• 300

• 150

• 180

• 210