Multiplication Counting Principle, Factorials and Permutations

Front

What is the Multiplication Counting Principle?

Back

The Multiplication 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 Factorial (n!).

Back

Factorial of a non-negative integer n, denoted as n!, is the product of all positive integers less than or equal to n. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120.

Front

What is a Permutation?

Back

A permutation is an arrangement of objects in a specific order. The number of permutations of 'n' distinct objects taken 'r' at a time is given by nPr = n! / (n - r)!.

Front

Calculate 5! (5 factorial).

Back

5! = 5 × 4 × 3 × 2 × 1 = 120.

Front

How many ways can 3 books be selected from 5 distinct books?

Back

Using the combination formula, the number of ways to choose 3 books from 5 is 5C3 = 5! / (3!(5-3)!) = 10.

Front

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

Back

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

Front

If a student can choose 4 different subjects from 10 available subjects, how many combinations are possible?

Back

Using the combination formula, the number of ways to choose 4 subjects from 10 is 10C4 = 210.

Front

How many different ways can the letters in the word 'BANANA' be arranged?

Back

The number of arrangements is 6! / (3! * 2!) = 60.

Front

What is the difference between permutations and combinations?

Back

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

Front

Calculate the number of ways to arrange 4 students in a line.

Back

The number of arrangements is 4! = 24.