Question

Most of the men of Delta Omicron Gamma play team sports, mostly on intramural teams but several on intercollegiate teams. Of the members, 18 play basketball, 20 play baseball, and 23 play football. Only 3 play all three sports; 9 play baseball and basketball; 8 play baseball and football; 10 play basketball and football. The other 14 members are involved in track, tennis, or swimming. How many men are in the DOG house? How many man play baseball only? How many men play football and baseball but do not play basketball?

Answer 1

There are 51 men in DOG.

Number of men who play baseball only are 2.

Number of men who play football and baseball but do not play basketball = 19

Explanation:

We can see from the Venn diagram attached,

n(A∩B∩F) = 3

n(A∩B) = 6

n(B∩F) = 5

n(A∩F) = 7

n(A∪B∪F) = n(A) + n(B) + n(F) - [n(A∩B) + n(A∩F) n(B∩F)] + n(A∩B∩F) + n(N)

= 20 + 18 + 23 - (9 + 8 + 10) + 3 + 14

= 61 - 27 + 17

= 51

Therefore, there are 51 men in DOG.

Number of persons who play baseball only = n(A) - [n(A∩B) + n(A∩F)] + n(A∩B∩C)

= 20 - (6 + 7 + 3)

= 20 - 16

= 2

Therefore, number of men who play baseball only = 2

Number of men who play football and baseball but do not play basketball

= 8 + 5 + 6

= 19

Therefore, number of men who play football and baseball but do not play basketball = 19