Set word problem3

In this page set word problem2 we will see how to solve the given problem. We use venn diagram to solve the problem. Using the same method student can try to solve the given practice problem.

There are 30 players in a group.10 play soccer, 12 play tennis, 15 play golf.  3 players play both soccer and tennis. 5 players play both tennis and golf. 4 players play both soccer and golf. 2 play all three games.

  1. Find how many play only soccer, only tennis and only golf?
  2. Find how many play none?


We will solve the problem using venn diagram. First let us write all the given information

        Universal set                           = 30

        Soccer players                        = 10

        Tennis players                         = 12

        Golf players                             = 15

        Playing both soccer and tennis    =   3

        Playing both tennis and golf        =   5

        Playing both soccer and golf        =   4

        Playing all three games               =   2

Here we have the universal set. To represent that we have to draw a rectangle. There are three classification, so we have to draw 3 overlapping circles S, T and G.

First we have to enter players playing all 3 games. This should be entered in the common overlapping area of all 3 circles.

There are 4 players playing both soccer and golf. Already we had entered 2. So we have to enter only 2(4-2=2) in the common area of the overlapping circles S and G. Similarly we have to enter 3(5-2=3) in the common area of T and G and 1(3-2=1) in the common area of S and T

Now  we have to enter the number of players who are playing golf. Already we had entered 7    ( 2+2+3)in the circle. So players who are playing only golf are 8(15-7). Similarly we can enter players playing only tennis (12-(1+2+3)) as 6 and players playing only soccer (10-(1+2+2)) as 5.

Now we can calculate the number of playing either soccer or tennis or golf. For that we have to add all the numbers inside the overlapping circles. 5+2+2+1+6+3+8=27. Now it is easy to calculate the players who plays none of the given games. For that we have to subtract 27 from the total 30. So 30-27=3 players who do not play any one of the given game.

From the final venn diagram we can get the answers for the given questions.


  • The number of players who play only soccer   =  5
  •  The number of players who play only tennis   =  6
  •   The number of players who play only golf     =   8

       2.  The number of players who play none of the

                                                       given game   =  3

Practice problem:

 A group of 30 children went to cafeteria.  6 ordered for ice cream 12 ordered for hot dogs and 15 ordered for burger. Only one student ordered for all 3 items. 3 ordered for ice cream and hot dogs, 3 ordered for ice cream and burger. 4 ordered for hot dog and burger.

  1. Find Number of students ordered only ice cream, hot dogs and burger?
  2. Find the number of students who ordered none?   

                                   Set word problems

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