Multiple Choice Questions on Basic Counting

Front

What is the Fundamental Counting Principle?

Back

The Fundamental 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

Define permutations.

Back

Permutations are arrangements of objects in a specific order. The number of permutations of 'n' objects taken 'r' at a time is given by n! / (n - r)!.

Front

Define combinations.

Back

Combinations are selections of objects without regard to the order. The number of combinations of 'n' objects taken 'r' at a time is given by n! / (r!(n - r)!).

Front

What is a factorial?

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.

Front

How do you calculate the number of ways to choose 'r' items from 'n' items?

Back

Use the combination formula: C(n, r) = n! / (r!(n - r)!).

Front

What is the difference between permutations and combinations?

Back

Permutations consider the order of selection, while combinations do not.

Front

What is the total number of outcomes when flipping a coin twice?

Back

There are 2^2 = 4 outcomes: HH, HT, TH, TT.

Front

How many different ways can you arrange the letters in the word 'MATH'?

Back

There are 4! = 24 different arrangements.

Front

If a die is rolled, what is the probability of rolling a number greater than 4?

Back

There are 2 favorable outcomes (5 and 6) out of 6 possible outcomes, so the probability is 2/6 = 1/3.

Front

What is the sample space for rolling two dice?

Back

The sample space consists of 36 outcomes, represented as (1,1), (1,2), ..., (6,6).