How many different signals are possible if we wish to make signals by arranging 3 red?

Solution of exercise 1

Find the total possible amount of eight-digit palindromic. Also, how many nine-digit palindromic are there? (Palindromic: a number whose digits read the same backwards and forwards.)

Solution of exercise 2

Four different math, six different physics and two different chemistry textbooks are placed on a shelf. What is the number of possible combinations of arranging the textbooks if:

The textbooks from each subject must be grouped together.

Only the math textbooks need to be grouped together.

Solution of exercise 3

A boy has five coins, each of a different value. How many different sums of money can be totaled with these five coins?

Solution of exercise 4

5 red, 2 white and 3 blue balls are arranged in a row. If the balls of like color are not distinguished from each other, how many possible ways can they be ordered?

Solution of exercise 5

With the dot and dash system of Morse code, how many different signals can be sent using four clicks or less?

The order of the elements does matter.

The elements can be repeated.

Solution of exercise 6

Eight people are seated at a dinner table at a political function. How many ways can they sit if the president and secretary always have to be seated next to one another?

There are two groups that the elements can be divided into for solving this problem. The first has two people (president and secretary) and the second has 7 people.

The order of the elements does matter.

The elements cannot be repeated.

Solution of exercise 7

How many diagonals does a pentagon have and how many triangles can be formed with its vertices?

First, the lines that can be drawn between 2 vertices need to be determined.

The order of the elements does not matter.

The elements cannot be repeated.

The sides that determine 5 straight lines that are not diagonal need to be subtracted.

Solution of exercise 8

In this example, we are given the following information:

The total number of candies = 8

Number of candies we want to select = 4

Is repetition allowed = No

The formula for calculating the permutations when no repetition is allowed is given below:

Substitute the values in the above formula to get the number of ways the candies can be selected:

Hence, we can select 4 candies from a set of 8 candies in 1680 ways.

Solution of exercise 9

In this example, we are given the following information:

The total number of vegetables = 10

Number of vegetables we want to select = 6

Is repetition allowed = No

The formula for calculating the permutations when no repetition is allowed is given below:

Substitute the values in the above formula to get the number of ways the candies can be selected:

Hence, we can select 6 vegetables from a set of 10 vegetables in 151200 ways.