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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. $3$
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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
(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;
+1 vote
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
+1 vote
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
+1 vote
Apply Mutual Exclusion -Inclusion principle

|(H U F)| = |(H)| + |(F)| - |(H^F)|

|(H U F)'| = |U| - |(H U F)|

Where |U| =25,  |H| = 15 , |F| = 17,  |H ^ F| = 10

|(H U F)| = 15 + 17 -10

|(H U F)| = 22

|(H U F)' |  = |U| - |(H U F)|

|(H U F)' | = 25 - 22

|(H U F)' | = 3

So Option (D) is right answer

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