Possibilities, Permutations, and Combinations

Front

What is the definition of a permutation?

Back

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

Front

What is the definition of 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

If you have 5 shirts and 3 pairs of pants, how many outfit combinations can you create?

Back

15 outfits (5 shirts x 3 pants = 15).

Front

What is the difference between permutations and combinations?

Back

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

Front

How many different 3-digit numbers can be formed using the digits 1, 2, 3, and 4 without repetition?

Back

24 different 3-digit numbers (4 options for the first digit, 3 for the second, and 2 for the third: 4 x 3 x 2 = 24).

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.

Front

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

Back

10 ways (C(5, 2) = 5! / (2! * 3!) = 10).

Front

If a password consists of 4 letters followed by 2 digits, how many different passwords can be created using 26 letters and 10 digits?

Back

The total is 26^4 * 10^2 = 45697600 different passwords.