Combinations and Arrangements Problems

Front

What is a combination?

Back

A combination is a selection of items from a larger set where the order does not matter.

Front

What is a permutation?

Back

A permutation is an arrangement of items from a larger set where the order does matter.

Front

How do you calculate combinations?

Back

Combinations are calculated using the formula: C(n, r) = n! / (r!(n-r)!), where n is the total number of items, and r is the number of items to choose.

Front

How do you calculate permutations?

Back

Permutations are calculated using the formula: P(n, r) = n! / (n-r)!, where n is the total number of items, and r is the number of items to arrange.

Front

What is the difference between combinations and permutations?

Back

The difference is that in combinations, the order of selection does not matter, while in permutations, the order does matter.

Front

How many ways can a club select a president, vice president, and a secretary from a group of 5 people?

Back

60 ways.

Front

How many ways can 18 runners be placed in first, second, and third?

Back

4896 ways.

Front

How many ways can Andy choose 5 candy bars from 14?

Back

2002 ways.

Front

How many different pizzas can you create with 8 meats, 4 cheeses, 3 crust types, and 2 sauces?

Back

192 different pizzas.

Front

What is the formula for calculating the number of ways to choose r items from n items?

Back

C(n, r) = n! / (r!(n-r)!)