# GATE2010-59

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$25$ persons are in a room. $15$ of them play hockey, $17$ of them play football and $10$ of them play both hockey and football. Then the number of persons playing neither hockey nor football is:

1. $2$
2. $17$
3. $13$
4. $3$

edited

D. 3
No. of persons who play either football or hockey $= 15 + 17 - 10 = 22$
No. of persons playing neither hockey nor football  $= 25 - 22 = 3$

selected by

Apply Principle of mutual Inclusion $-$Exclusion

$n(A\cup B)=n(A)+n(B)-n(A\cap B)$

edited
1
this is more understandable than other methods, as this can be used in any other this type of questions, i was just looking for this kind of solution, Thank You
(D)3;

Explanation- number of player=25,

player who play either football or hockey=17+15,

play both hockey and football=10.

then players who play=32-10=22

then players who do not play =25-22=3;
no.of persons only play hockey =15-10=5
no. of persons only play  football =17-10=7
no.of persons play both hockey and football=10
so,total no of persons play hockey and football =5+7+10=22
therefore,total no. of persons neither play hockey nor football=25-22=3
25 person

hockey = 15 =  15-10= 5

football = 17= 17-10=7

both= 10

neither football and hockey= 25-(7+5+10)=25-22=3

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