Counting Principle

Front

What is the Counting Principle in combinatorics?

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 lunches can be made if a student can choose one sandwich, one salad, and one piece of fruit from given options?

Back

To find the total combinations, multiply the number of choices for each category: 3 sandwiches × 2 salads × 3 fruits = 18 different lunches.

Front

What is the formula to calculate the number of ways to choose 'r' items from 'n' items without regard to the order?

Back

The formula is given by the binomial coefficient: C(n, r) = n! / (r!(n-r)!) where '!' denotes factorial.

Front

If there are 9 types of ice cream and 4 friends, how do you calculate the probability that each friend orders a different type?

Back

Calculate the total arrangements of 9 types taken 4 at a time (P(9, 4)) and divide by the total possible orders (9^4). The probability is 336/729.

Front

How many different Personal Identification Numbers (PINs) can be created with 2 letters followed by 2 digits if repetition is allowed?

Back

The number of PINs is calculated as: 26^2 (for letters) × 10^2 (for digits) = 67600.

Front

What is the total number of possible 4-digit PIN codes?

Back

Each digit can be any number from 0 to 9, so the total is 10^4 = 10,000 possible PIN codes.

Front

How many ways can a quiz with 3 true/false questions be completed?

Back

Each question has 2 possible answers (true or false), so the total ways to complete the quiz is 2^3 = 8.

Front

What is the difference between permutations and combinations?

Back

Permutations consider the order of selection, while combinations do not. For example, choosing 3 out of 5 items in order is a permutation, while choosing without regard to order is a combination.

Front

How do you calculate the total number of outcomes in a scenario with multiple independent choices?

Back

Multiply the number of outcomes for each independent choice together.

Front

What is a factorial and how is it denoted?

Back

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