Counting Principles

Front

What are counting principles in mathematics?

Back

Counting principles are rules and methods used to count the number of ways an event can occur, often involving combinations and permutations.

Front

How do you calculate the total number of outfits from different clothing items?

Back

Multiply the number of choices for each clothing item together. For example, if you have 4 pairs of shoes, 5 colors of socks, 8 pairs of pants, and 15 shirts, the total outfits = 4 * 5 * 8 * 15.

Front

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

Back

The formula is P(n, r) = n! / (n - r)!, where n is the total number of items and r is the number of items to arrange.

Front

What is the formula for combinations of n items taken r at a time?

Back

The formula is C(n, r) = n! / (r! * (n - r)!), where n is the total number of items and r is the number of items to choose.

Front

How many different license plates can be made with 2 letters followed by 3 digits without repetition?

Back

The total is calculated as 26 * 25 (for letters) * 10 * 9 * 8 (for digits) = 26 * 25 * 10 * 9 * 8.

Front

What is the binary representation of the decimal number 18?

Back

The binary representation of 18 is 10010.

Front

How do you calculate the number of combinations for initials and birth year digits?

Back

Multiply the number of choices for each initial (26 for each) and for each digit (10 for each), resulting in 26 * 26 * 26 * 10 * 10.

Front

What is the factorial of a number and how is it denoted?

Back

The factorial of a number n, denoted as n!, is the product of all positive integers up to n. For example, 5! = 5 * 4 * 3 * 2 * 1 = 120.

Front

How many ways can a coach arrange the batting order of 9 players?

Back

The number of arrangements is calculated as 9! (9 factorial), which equals 362880.

Front

What is the difference between permutations and combinations?

Back

Permutations consider the order of selection, while combinations do not. For example, arranging 3 letters (A, B, C) as ABC is different from ACB in permutations but the same in combinations.