Permutations and Combinations Problems

This video tutorial on the TechMath channel explores combinations and permutations through six practical examples. It covers how to determine whether a problem is a combination or permutation, and demonstrates solving each type of problem with real-world scenarios such as song selection, horse racing, card dealing, arranging letters, fruit selection, and seating arrangements around a campfire. The video emphasizes understanding the importance of order in permutations and how to handle repeated elements in arrangements.

What is the main difference between combinations and permutations?

• Combinations consider order, permutations do not.

• Permutations consider order, combinations do not.

• Both consider order.

• Neither consider order.

In a permutations problem, how does the order of selection affect the outcome?

• Order affects the outcome only if specified.

• Order only affects the outcome if there are more than 10 items.

• Order does not affect the outcome.

• Order affects the outcome significantly.

How many different ways can a person perform 3 songs from a choice of 7?

• 210

• 35

• 5040

• 120

In a horse race with 12 horses, how many ways can the first, second, and third places be determined?

• 504

• 720

• 1320

• 220

If order does not matter in selecting the top 3 horses from a race of 12, how many combinations are possible?

• 220

• 720

• 1320

• 504

How many different ways can 5 cards be dealt from a deck of 52 cards?

• 10,200

• 52,000

• 311,875,200

• 2,598,960

In the word 'Mississippi', how many unique permutations can be formed?

• 20,000

• 34,650

• 46,656

• 11,000

How many ways can 4 fruits be selected from a group of 6?

• 10

• 30

• 20

• 15

How many different ways can 6 people sit around a campfire?

• 720

• 240

• 120

• 360