To find the number of people who prefer different combinations of songs based on the information provided, we can use a Venn diagram.
(i) Number of people who prefer at least one type of song:
To find this, we need to consider the total number of people who prefer modern, classic, or folk songs. We can add the number of people who prefer each type of song and then subtract the number of people who prefer two types of songs (double-counted) and add back the number of people who prefer all three types of songs to avoid undercounting.
(ii) Number of people who prefer all three types of songs:
This can be found by looking at the center of the Venn diagram where all three circles intersect. The value at this intersection represents the number of people who prefer all three types of songs.
(iii) Number of people who prefer only two types of songs:
To find this, we can add the number of people who prefer modern and classic, classic and folk, and modern and folk songs. Then we subtract the number of people who prefer all three types of songs to get the total number of people who prefer only two types of songs.
By following these steps and accurately placing the values in the Venn diagram, you can calculate the number of people who prefer different combinations of songs as specified in the question.
