Counting Principle and Permutations

Front

What is the Counting Principle?

Back

The Counting Principle states that if there are 'm' ways to do one thing and 'n' ways to do another, then there are m × n ways to do both.

Front

How many different lunch combinations can be made with 6 sandwiches, 3 types of chips, and 5 beverages?

Back

270 combinations (6 × 3 × 5 = 90).

Front

What is a permutation?

Back

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

Front

How many possible outcomes are there when rolling two dice?

Back

36 outcomes (6 sides on the first die × 6 sides on the second die = 36).

Front

How many different pizzas can be made with 8 meats, 4 cheeses, 3 crust types, and 2 sauces?

Back

192 different pizzas (8 × 4 × 3 × 2 = 192).

Front

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

Back

The formula is n! / (n - r)!.

Front

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

Back

12 two-digit numbers (4 choices for the first digit and 3 choices for the second digit: 4 × 3 = 12).

Front

What is the difference between combinations and permutations?

Back

Combinations are selections where order does not matter, while permutations are arrangements where order does matter.

Front

How many meal combinations can be made with 2 salads, 3 entrees, and 2 beverages?

Back

12 meal combinations (2 × 3 × 2 = 12).

Front

What is factorial notation (n!)?

Back

Factorial notation (n!) represents the product of all positive integers up to 'n'.