Permutation and Combination

Front

What is a permutation?

Back

A permutation is an arrangement of objects in a specific order. The order matters in permutations.

Front

What is a combination?

Back

A combination is a selection of objects where the order does not matter. Only the group of objects is important.

Front

How do you calculate permutations of n objects taken r at a time?

Back

The formula is P(n, r) = n! / (n - r)!, where n is the total number of objects and r is the number of objects to arrange.

Front

How do you calculate combinations of n objects taken r at a time?

Back

The formula is C(n, r) = n! / [r!(n - r)!], where n is the total number of objects and r is the number of objects to choose.

Front

What is the difference between permutations and combinations?

Back

Permutations consider the order of selection, while combinations do not.

Front

If a team has 12 players and 10 are selected for the batting order, how many ways can this be done?

Back

C(12, 10) = 66 ways.

Front

In how many ways can 3 students be selected from a group of 19?

Back

C(19, 3) = 969 ways.

Front

If Micaela has homework in 6 subjects, how many different orders can she complete them?

Back

6! = 720 different orders.

Front

How many ways can a captain and co-captain be chosen from 15 players?

Back

P(15, 2) = 15! / (15 - 2)! = 210 ways.

Front

What is the factorial of a number?

Back

The factorial of a number n (denoted as n!) is the product of all positive integers up to n.