Understanding Combinations and Permutations

Front

What is the definition of a combination in mathematics?

Back

A selection of objects without regard to the order.

Front

Differentiate between combinations and permutations.

Back

Permutations consider order, combinations do not.

Front

Which of the following is a permutation problem? (a) Choosing 3 desserts from a menu of 10. (b) Arranging 5 books on a shelf. (c) Selecting 4 team members from a group of 12. (d) Picking 2 colors from a palette of 8.

Back

Arranging 5 books on a shelf.

Front

In how many ways can a committee of 4 be formed from 10 people?

Back

210

Front

Which of the following scenarios is an example of a combination? (a) Arranging books on a shelf. (b) Selecting a committee from a group. (c) Assigning seats to students. (d) Creating a password with specific characters.

Back

Selecting a committee from a group.

Front

What is the formula for calculating combinations?

Back

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

What is the formula for calculating permutations?

Back

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

Front

If you have 5 different books, how many ways can you arrange them on a shelf?

Back

120 ways (5!).

Front

How many ways can you choose 2 fruits from a selection of 5 different fruits?

Back

10 ways (C(5, 2)).

Front

What is the difference between 'selecting' and 'arranging' in the context of combinations and permutations?

Back

Selecting refers to combinations (order does not matter), while arranging refers to permutations (order matters).