Combinations

This video tutorial covers the concept of combinations in probability and statistics, contrasting them with permutations. It explains that in combinations, the order of elements does not matter, unlike permutations where order is crucial. The tutorial provides examples to illustrate these differences and introduces the formula for calculating combinations. It also includes problem-solving exercises to help viewers understand when to apply combinations versus permutations.

What is the primary difference between permutations and combinations?

• Combinations involve repetition, permutations do not.

• Order matters in permutations, but not in combinations.

• Order matters in combinations, but not in permutations.

• Permutations involve repetition, combinations do not.

In a race with 3 runners, how many ways can you arrange the first and second place?

• 3

• 6

• 9

• 12

When selecting 2 people from a group of 3 to attend a conference, how many combinations are possible?

• 4

• 2

• 1

• 3

Which formula is used to calculate combinations?

• r! / (n!(n-r)!)

• n! / (r!(n-r)!)

• n! / (n-r)!

• (n-r)! / n!

Why are there fewer combinations than permutations for the same set of elements?

• Permutations do not consider order.

• Combinations allow repetition.

• Permutations allow repetition.

• Combinations do not consider order.

What is the result of dividing permutations by r! in the context of combinations?

• It doubles the number of combinations.

• It has no effect on the number of combinations.

• It decreases the number of combinations.

• It increases the number of combinations.

In the context of combinations, what does the term 'binomial coefficient' refer to?

• A way to simplify factorials.

• A method to calculate permutations.

• A way to expand algebraic expressions.

• A method to calculate combinations.

In a lottery where you pick 6 numbers from 49, why is it a combination problem?

• The order of numbers does not matter.

• Only one number can be picked at a time.

• The order of numbers matters.

• Repetition of numbers is allowed.

How many ways can you choose 2 warehouses from 20?

• 220

• 190

• 200

• 210

If a manufacturer has 8 motors and 5 switches, how many ways can they select 2 motors and 2 switches?

• 280

• 300

• 320

• 340