Of the members of three athletic teams in a certain school, 21 are in the basketball team, 26 in hockey team and 29 in the football team. 14 play hockey and basket ball, 15 play hockey and football, 12 play football and basketball and 8 play all the three games bow many members are there in all?

Answer

43

Explanation

`a + f + e + g = 21 " … (i)"`
b + d + f + g = 26 … (ii)
c + d + e + g = 29 … (iii)
f + g = 14 … (iv)
g + d = 15 … (v)
e + g = 12 … (vi)
g = 8 … (vii)

From Eqs. (vii) and (vi), e = 4
Form Eqs. (vii) and (v), d = 7
From Eqs. (vii) and (iv), f = 6
From Eq. (iii), c + 7 + 4 + 8 = 29 implies c = 29 - 19 = 10 = c
From Eq. (ii), b + 7 + 6 + 8 = 26 implies b = 26 - 21 implies b = 5
From Eq. (i), a + 6 + 4 + 8 = 21 implies a = 21 - 18 implies a = 3
`n(B) + n(H) + n(F) = a+b+c+d+e+f+g=3+5+10+7+4+6+8=43`