Understanding Random Variables and Counting

Which of the following best defines a discrete random variable?

• A variable that can take on any value within a given range.

• A variable that can take on a countable number of distinct values.

• A variable that is always positive.

• A variable that is always negative.

Which of the following best defines a continuous random variable?

• A variable that can take on any value within a given range.

• A variable that can only take integer values.

• A variable that is always positive.

• A variable that is always negative.

How many different ways can you arrange the letters in the word "QUIZ"?

• 12

• 24

• 48

• 120

If you have 5 different books, how many ways can you arrange 3 of them on a shelf?

• 10

• 20

• 60

• 120

In how many ways can you choose 3 students from a group of 10 to form a committee?

• 30

• 60

• 120

• 720

What is the main difference between permutations and combinations?

• Permutations consider order, combinations do not.

• Combinations consider order, permutations do not.

• Both consider order.

• Neither consider order.

Using the counting principle, how many different outfits can you create with 3 shirts and 4 pants?

• 7

• 12

• 15

• 24

Calculate the number of permutations of the letters in the word "MATH".

• 12

• 16

• 24

• 32

If a password consists of 3 letters followed by 2 digits, how many different passwords can be created if repetition is allowed?

• 676,000

• 1,757,600

• 1,000,000

• 1,757,000

How many ways can you select 2 cards from a standard deck of 52 cards?

• 1,326

• 2,652

• 1,000

• 2,500