Permutations, Combination, and Counting (Take 2)

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.

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)!.

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)!].

Front

If you have 5 books and want to arrange them on a shelf, how many different arrangements can you make?

Back

120 arrangements (5! = 5 × 4 × 3 × 2 × 1 = 120).

Front

In how many ways can you choose 3 students from a group of 10?

Back

The answer is 120 ways (C(10, 3) = 10! / [3!(10 - 3)!]).

Front

What is the difference between permutations and combinations?

Back

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

Front

If you have 4 different shirts and 2 pairs of pants, how many outfits can you create?

Back

8 outfits (4 shirts × 2 pants = 8).

Front

How many ways can you select 2 ice cream flavors from 10 available flavors if the order does not matter?

Back

The answer is 45 ways (C(10, 2) = 10! / [2!(10 - 2)!]).

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.