Permutations, Combinations and Probability Flashcard

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 the number of 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 the number of 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 factorial of a number?

Back

The factorial of a number n (denoted as n!) is the product of all positive integers up to n. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120.

Front

How many distinct arrangements can be made with the letters in the word 'OPPORTUNITIES'?

Back

The number of distinct arrangements is 389,188,800.

Front

If there are 45 applicants for 3 job positions, is this a permutation or combination?

Back

This is a combination because the order of selection does not matter.

Front

If a team of 8 basketball players needs to choose a captain and co-captain, is this a permutation or combination?

Back

This is a permutation because the order of selection matters (captain vs co-captain).

Front

How many ways can Michael choose 5 flowers from a list of 8?

Back

Michael can create 56 different bouquets.

Front

How many different seating charts are possible for 17 students?

Back

There are 3.6 x 10^14 different seating charts possible.