Permutations and Combinations

What does the notation P(n,r) represent?

• The number of r-permutations of a set with n elements

• The number of r-combinations of a set with n elements

• The number of permutations with repetition of a set with n elements

• The number of ways to choose r elements from a set with n elements

How many permutations are there of a set of 3 elements taken 3 at a time with repetition?

• 9

• 6

• 27

• 81

Which of the following is an example of a permutation without repetition?

• Choosing 3 scoops of ice cream from 5 flavors

• Choosing 4 students out of a class of 20 to form a team

• Arranging 5 books on a shelf

• Selecting 3 pieces of fruit from 6 types

How many 4-letter codes can be formed using the letters A, B, and C if repetition is allowed?

• 12

• 24

• 64

• 81

What does the notation C(n,k) represent?

• The number of k-permutations of a set with n elements

• The number of k-combinations of a set with n elements

• The number of combinations with repetition of a set with n elements

• The number of ways to choose n elements from a set with k elements

A _____ of a set is an arrangement of its members into a sequence or linear order. The number of ways to arrange n objects in order is denoted as P(n,r), where r is the number of objects chosen from the set.

• Combination

• Factorial

• Elements

• Permutation

A _____ is a selection of items from a larger pool where order does not matter. The number of ways to choose k items from n items is denoted as C(n, k).

• Combination

• Factorial

• Elements

• Permutation

_____ is the product of all positive integers up to n. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120.

• Combination

• Factorial

• Elements

• Permutation

The total number of elements in the set from which selections or arrangements are being made.

• P

• C

• n

• r

The number of elements chosen from the total set for permutations or combinations.

• P

• C

• n

• r