Combinations ,Permutations, Factorial, Counting Principle Review

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

What is a factorial?

Back

A factorial, denoted as n!, is the product of all positive integers from 1 to n.

Front

How do you calculate the number of combinations of choosing r items from n items?

Back

The formula is C(n, r) = n! / (r!(n-r)!).

Front

How do you calculate the number of permutations of choosing r items from n items?

Back

The formula is P(n, r) = n! / (n-r)!.

Front

What is the counting principle?

Back

The counting principle states that if one event can occur in m ways and a second can occur independently in n ways, then the two events can occur in m × n ways.

Front

How many ways can you choose 2 candidates from 7 candidates?

Back

C(7, 2) = 7! / (2!(7-2)!) = 21 ways.

Front

How many ways can you arrange 3 books from a shelf of 5 books?

Back

P(5, 3) = 5! / (5-3)! = 60 ways.

Front

If you have 4 different toppings and want to choose 2, how many combinations can you make?

Back

C(4, 2) = 4! / (2!(4-2)!) = 6 combinations.

Front

How many different ways can you select a president and a vice-president from 10 members?

Back

P(10, 2) = 10! / (10-2)! = 90 ways.