Permutations and Combinations

Front

What is a permutation?

Back

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

Front

What is a combination?

Back

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

Front

How do you calculate the number of permutations of n objects?

Back

The number of permutations of n objects is calculated as n! (n factorial), which is the product of all positive integers up to n.

Front

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

Back

The number of combinations is calculated using the formula: 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

If you have 5 pairs of jeans, 8 t-shirts, and 2 pairs of shoes, how many outfits can you create?

Back

80 outfits (5 * 8 * 2 = 80).

Front

How many different codes can be formed with one digit and one letter, excluding 0 and O?

Back

225 codes (9 digits * 25 letters = 225).

Front

How many ways can the letters in the word 'MATH' be arranged?

Back

24 ways (4! = 24).

Front

A restaurant offers 4 sizes of pizza, 2 types of crust, and 8 toppings. How many combinations of pizza with one topping are possible?

Back

64 combinations (4 sizes * 2 crusts * 8 toppings = 64).

Front

How do you choose a manager and assistant from a group of 9 people?

Back

You can choose in 72 ways (9 choices for manager * 8 choices for assistant = 72).

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 from 1 to n.