Counting Principle Permutations Combinations Flashcard

Front

What is the Counting Principle?

Back

The Counting Principle states that if one event can occur in 'm' ways and a second event can occur independently in 'n' ways, then the two events can occur in 'm × n' ways.

Front

Define Permutations.

Back

Permutations are arrangements of objects where the order matters. For example, the arrangements of the letters A, B, and C are ABC, ACB, BAC, BCA, CAB, and CBA.

Front

Define Combinations.

Back

Combinations are selections of objects where the order does not matter. For example, the combinations of the letters A, B, and C taken two at a time are AB, AC, and BC.

Front

How many ways can you arrange 3 books on a shelf?

Back

6 ways (3! = 3 × 2 × 1 = 6).

Front

What is the formula for permutations of 'n' objects taken 'r' at a time?

Back

The formula is P(n, r) = n! / (n - r)!.

Front

What is the formula for 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 different shirts and 3 different pants, how many outfits can you create?

Back

15 outfits (5 shirts × 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 ways can you choose 2 toppings from 5 available toppings for a pizza?

Back

10 ways (C(5, 2) = 5! / [2!(5 - 2)!] = 10).

Front

What is the total number of combinations for a combination lock with 3 digits (0-49)?

Back

125,000 combinations (50^3 = 125,000).