Introduction to Counting Principles

Front

What is the Fundamental Counting Principle?

Back

The Fundamental Counting Principle states that if one event can occur in 'm' ways and a second event can occur independently in 'n' ways, then the two events can occur in m × n ways.

Front

How many ways can you select a president, a vice-president, and a secretary from a group of 5 people if no person can hold more than one position?

Back

60

Front

How many ways can 5 students stand in a line?

Back

120

Front

What is a permutation?

Back

A permutation is an arrangement 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

How many 2-digit numbers can be formed using the digits 1, 2, 3, and 4 if repetition is not allowed?

Back

12

Front

What is a combination?

Back

A combination is a selection of items from a larger set where the order does not matter. The number of combinations of 'n' items taken 'r' at a time is given by n! / (r!(n - r)!).

Front

If you have 4 shirts and 3 pairs of pants, how many different shirt and pant combinations can you make?

Back

12

Front

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

Back

6

Front

What is the formula for calculating permutations of 'n' items?

Back

The formula for permutations of 'n' items is n!.

Front

What is the difference between permutations and combinations?

Back

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