Exercise 4

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Adrian Paul C. Hernane

2 – BSECE – A

Exercise #4

Permutation

A way of arranging certain set of numbers and things in an orderly manner.

Example:

In how many ways can you arrange the letters in the word STYLE?

➢ To find the number of ways we can arrange the word style, we will use the

concept of permutation.

➢ Basically we have 5 letters on the word style. So, we need to arrange them

without repeating another letter.

➢ Therefore, the formula would be like:

Let: n = number in a group = 5

➢ The formula above was also known as “n!” (n factorial). In every position of the

letter, we subtract those that were already used in the previous positions. For

letter #1, we didn’t subtract since every letter has the chance to be on that

position. On letter #2, we subtract a number since the first letter was already

used and cannot be repeated. This process continues until the last position.

For better understanding, we will illustrate it like this:

n-1

n-2

n-3

n-4

Letter #1

Letter #2

Letter #3

Letter #4

Letter #5

S T Y L E

T Y L E

Y L E

L E

position

➢ Just like the figure above, as every letter position is occupied, the letter that has

already a position won’t be repeated. This sequence will continue until every

position is filled. That is how we solve for the permutation.

➢ The result of the problem would be:

5! = 5 x 4 x 3 x 2 x 1

5! = 120

➢ There are 120 ways you can arrange the letters in the word STYLE.

Combination

Is the way of selecting objects and numbers in a group of objects or collections in

which the order does not matter.

Example:

How many combinations of 3 colour boxes can you make out of 4 different

coloured boxes?

➢ In this example, the concept of combination will be used since the problem

doesn’t require the order of the combinations.

➢ What we do in this problem is to use the formula for combination:

 











n = number in a group

r = number taken in a group

➢ We can also illustrate it for better understanding. The problem states that there

are four coloured boxes. Among those, we will pick only three coloured boxes.

➢ Finding the combination with the use of the formula will be easy. However, we

will manually find the combination. Just keep in our minds that the order of the

coloured boxes doesn’t matter. We will also find the combinations through the

formula.

Box 1

Box 2

Box 3

Box 4

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Adrian Paul C. Hernane 2 – BSECE – A Exercise #4 Permutation A way of arranging certain set of numbers and things in an orderly manner. Example: In how many ways can you arrange the letters in the word STYLE? ➢ To find the number of ways we can arrange the word style, we will use the concept of permutation. ➢ Basically we have 5 letters on the word style. So, we need to arrange them without repeating another letter. ➢ Therefore, the formula would be like: Let: n = number in a group = 5 n n-1 n-2 n-3 n-4 Letter #1 Letter #2 Letter #3 Letter #4 Letter #5 ➢ The formula above was also known as “n!” (n factorial). In every position of the letter, we subtract those that were already used in the previous positions. For letter #1, we didn’t subtract since every letter has the chance to be on that position. On letter #2, we subtract a number since the first letter wa ...
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