In a group of girls, 20 play volleyball, 21 play badminton and 18 play table tennis; 7 play volleyball only; 9 play badminton only; 6 play volleyball and badminton only and 2 play badminton and table-tennis only.
a)How many play all three games?
b)How many play volleyball and table-tennis only?
c)How many play table-tennis only?
d)How many girls are there altogether?
IN A CLASS OF 36 GIRLS,18 PLAY NET BALL , 16 PLAY TABLE TENNS WHILE 8 GIRLS PLAY NEITHER THE TWO GAMES. FIND THE NUMBER OF GIRLS WHO PLAY
To answer these questions, we can use the principle of inclusion-exclusion. We will start by finding the number of girls who play at least one of the three games, and then use this information to answer each question.
Let's denote:
V = number of girls who play volleyball
B = number of girls who play badminton
T = number of girls who play table tennis
We are given the following information:
1) Number of girls who play volleyball = 20
2) Number of girls who play badminton = 21
3) Number of girls who play table tennis = 18
4) Number of girls who play volleyball only = 7
5) Number of girls who play badminton only = 9
6) Number of girls who play volleyball and badminton only = 6
7) Number of girls who play badminton and table tennis only = 2
Now, let's find the number of girls who play at least one of the three games.
Step 1: Calculate the number of girls who play at least two games.
a) Number of girls who play volleyball and badminton = Number of girls who play volleyball and badminton only + Number of girls who play volleyball, badminton, and table tennis only
= 6 + 0 (since there are no girls who play all three games only)
= 6
b) Number of girls who play badminton and table tennis = Number of girls who play badminton and table tennis only + Number of girls who play volleyball, badminton, and table tennis only
= 2 + 0 (since there are no girls who play all three games only)
= 2
Step 2: Calculate the number of girls who play exactly one game.
a) Number of girls who play volleyball only = 7
b) Number of girls who play badminton only = 9
c) Number of girls who play table tennis only = Number of girls who play table tennis - Number of girls who play badminton and table tennis only
= 18 - 2
= 16
Now, let's answer each question using the obtained information.
a) Number of girls who play all three games = Number of girls who play volleyball, badminton, and table tennis only
= 0 (since there are no girls who play all three games only)
b) Number of girls who play volleyball and table-tennis only = Number of girls who play volleyball only + Number of girls who play volleyball and badminton only + Number of girls who play volleyball, badminton, and table tennis only
= 7 + 6 + 0
= 13
c) Number of girls who play table tennis only = Number of girls who play table tennis only + Number of girls who play volleyball, badminton, and table tennis only
= 16 + 0
= 16
d) Number of girls altogether = Number of girls who play volleyball + Number of girls who play badminton + Number of girls who play table tennis - Number of girls who play exactly two games + Number of girls who play all three games
= 20 + 21 + 18 - (6 + 2) + 0
= 51
Therefore, the answers to the given questions are:
a) 0 girls play all three games.
b) 13 girls play volleyball and table tennis only.
c) 16 girls play table tennis only.
d) There are 51 girls altogether.