Permutations, Combinations, and Probability

This video tutorial covers the basic counting principles, permutations, and combinations, along with their applications in probability. It explains the multiplication rule for counting, how to calculate permutations when order matters, and combinations when order does not matter. The tutorial includes practical examples, such as calculating possible code combinations and determining probabilities in card games, and demonstrates using a TI-84 calculator for these calculations.

How many possible 4-digit codes can be created using digits 0-9 if repetition is allowed?

• 1,000

• 10,000

• 5,040

• 100

What is the value of 5 factorial (5!)?

• 24

• 60

• 120

• 720

In permutations, what is the key factor that differentiates it from combinations?

• Replacement is allowed

• Order matters

• Repetition is allowed

• Order does not matter

How many ways can 8 athletes be awarded first, second, and third place?

• 120

• 720

• 336

• 56

If repetition is not allowed, how many 3-letter words can be formed from the letters F, G, H, I, J?

• 125

• 60

• 10

• 30

What is the formula for calculating combinations?

• n! / r!

• n! / (r!(n-r)!)

• n! / (n-r)!

• (n-r)! / n!

In a lottery game, how many ways can a player pick 3 numbers from 0 to 9 if order does not matter?

• 84

• 720

• 120

• 56

How many different 5-card hands can be dealt from a deck of 52 cards?

• 10,000

• 52,000

• 1,000,000

• 2,598,960

What is the probability of drawing exactly four aces in a 5-card poker hand?

• 0.0609%

• 0.0495%

• 1%

• 0.0018%

If you want to draw exactly two aces and two kings in a 5-card hand, what is the probability?

• 0.0018%

• 0.1%

• 0.0609%

• 0.0495%