Question

A certain college has 52 students participating in games.30 play netball, 25 play football , 10 play handball and football ,13 play netball and handball,9 play netball and football while 2 play all the three games. How many students play handball and no other game?  

Answer 1

Draw Venn diagram

$$n(Nb\cup Fb\cup Hb)=52$$

$$n(Nb)=30, n(Fb)=25$$

$$n(Hb\cap Fb)=10, n(Nb\cap Hb)=13,$$

$$n(Nb\cap Fb)=9, n(Nb\cap Hb\cap Fb)=2$$

$$n(Nb\cup Hb\cup Fb)=n(Nb)+n(Hb)+n(Fb)$$

$$-n(Nb\cap Hb)-n(Nb\cap Fb)-n(Hb\cap Fb)$$

$$+n(Nb\cap Hb\cap Fb)$$

$$52=30+n(Hb)+25-10-13-9+2$$

$$n(Hb)=27$$

$$27-11-2-8=6$$

6 students play handball and no other game.