In a class of 75, each student is enrolled for at least one of the

Question

In a class of 75, each student is enrolled for at least one of the three sports - Soccer, Hockey, or Baseball. 39 students are enrolled for Soccer, 29 are enrolled for Hockey, and 35 are enrolled for Baseball. If 7 students are enrolled for all the three, how many students are enrolled for exactly two of the three sports?

A. 7
B. 14
C. 17
D. 21
E. 28

A. 7
B. 14
C. 17
D. 21
E. 28

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chloreton · Answer

Here None =0 (since each player is enrolled for atleast one sport) and let 2 group overlap be 'x'
Total = A+B+C-(2 group overlap)-2*(3 group overlap)+None
75=39+29+35-x-2*7+0
Solving for x we get x=14

Therefore, Option  (B)

Dereno · Answer

I represent exactly one sport

II represent exactly two sports

III represent exactly three sports.

I +II + III = 75 ———(1)

None = 0

If , we add all the values of the set we get

I +2II + 3III = (39+29+35) = 103

I +2II + 3III = 103 ———-(2)

Subtracting equations 1 and 2, we get

II + 2III =28.

Given all three sport = III = 7

II =  14

Option B

vasu1104 · Answer

total = 75
soccer= 39
hockey = 29 
baseball=35
only soccer= 32-a-c
only hockey= 22-a-b
only baseball = 28-b-c
soccer and hockey = a
hockey and baseball = b
baseball and soccer =c
all three = 7
neither= 0

32-a-c+22-c-b+28-b-c+a+b+c+7 = 75
a+b+c= 14

egmat · Answer

We have  75  students, and each student plays at least one sport among Soccer, Hockey, or Baseball. We need to find how many students play  exactly two  sports.

Given Information: 
• Total students =  75 
• Soccer =  39 
• Hockey =  29 
• Baseball =  35 
• All three sports =  7

Total = (Sum of individual groups) - (Sum of pairwise overlaps) + (All three)

75  =  39  +  29  +  35  - (Sum of pairwise overlaps) +  7

75  =  110  - (Sum of pairwise overlaps)

Sum of pairwise overlaps =  110  -  75  =  35

When we calculate pairwise overlaps (Soccer & Hockey, Hockey & Baseball, Soccer & Baseball), we are counting the "all three" students in EACH pair!

Think about it: A student who plays all three sports gets counted:
• Once in (Soccer & Hockey)
• Once in (Hockey & Baseball)
• Once in (Soccer & Baseball)

That's  3  times!

Therefore: 
Sum of pairwise overlaps = (Exactly two sports) +  3  × (All three sports)

35  = (Exactly two sports) +  3  ×  7

35  = (Exactly two sports) +  21

Exactly two sports =  35  -  21  =  14

Answer: B

ExpertsGlobal5 · Answer

Video explanation:    https://www.youtube.com/watch?v=l9Wq2j0sYR8

Soumya_Pinjala · Answer

I have tried to solve this by formula n(a U b U C ) =n (A) + n(B) + n(c) - n(A intersection B) - n(B intersection C) - n( C intersection A) + n( A intersection B intersection C) . This formula already handles subtracting the terms that are counted twice. Why are we subtracting again when it’s already handled by the formula

In a class of 75, each student is enrolled for at least one of the

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