FCP, Combinations, and Permutations

Front

What is a Permutation?

Back

A permutation is an arrangement of objects in a specific order. The order matters in permutations.

Front

What is a Combination?

Back

A combination is a selection of items without regard to the order. The order does not matter in combinations.

Front

What is the Fundamental Counting Principle (FCP)?

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 5 people be arranged in a line?

Back

5! = 120 ways (Permutation) because the order of arrangement matters.

Front

If you have 10 different books and want to choose 3 to read, how many combinations can you make?

Back

The number of combinations is calculated as 10C3 = 120.

Front

In how many ways can you select a president, vice president, and secretary from a group of 5 people?

Back

This is a permutation problem: 5P3 = 60 ways.

Front

What is the difference between permutations and combinations?

Back

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

Front

If a committee of 4 is to be formed from a group of 10 people, how many different committees can be formed?

Back

10C4 = 210 different committees (Combination).

Front

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

Back

4! = 24 ways (Permutation).

Front

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

Back

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