Mastering Permutations and Combinations

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. It focuses on the group rather than the arrangement.

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

In how many different ways can a president, vice-president, treasurer, historian, and secretary be selected from 24 members?

Back

5,100,480 ways.

Front

Is selecting a lead and an understudy for a school play a permutation or a combination?

Back

It is a permutation because the order of selection matters.

Front

How many different committees of 4 can be formed from a group of 7 people?

Back

35 different committees.

Front

In a race with 10 participants, how many ways can the top 3 finishers be arranged?

Back

720 ways.

Front

If you have 8 different books, how many ways can you arrange 3 of them on a shelf?

Back

336 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.