n(a or b or c) = n(a) + n(b) + n(c) - n(a&b) - n(b&c) - n(c&a) +(a&b&c)
given: There are 60 people. So
n(a or b or c) = 60.
48 invested in A, 35 invested in B, and 27 invested in C. So..
n(a) = 48
n(b) = 35
n(c) = 27.
among 19 of people who invested in both A and C, 12 also invested in B. So..
n(a&c) = 19 but n(a&b&c) = 12. therefore only n(a&c) = 7.
All people who invested in B also invested in A. So..
n(a&b) = 35. but n(a&b&c) = 12..so only n(a&b) = 23. also only n(b) = 0, only n(b&c) = 0. and
finally only n(c) = 8
[n(c) = only n(c) + only n(a&c) + only n(b&c) + n(a&b&c)]
likewise only n(b) =0
[n(b) = only n(b) + only n(a&b) + only n(b&c) + n(a&b&c)]
likewise only n(a) =6
[n(a) = only n(a) + only n(a&b) + only n(a&c) + n(a&b&c)]
Therefore...Finally..phew....
n(a or b or c) = only n(a) + only n(b) + only n(c) + only n(a&b)+ only n(b&c)+ only n(a&c)+ n(a&b&c)
6+0+8+23+0+7+12 = 56.
this means that people who invest in atleast one plan is 56.
therefore ppl who dont invest in any is 60-54 = 4.
i know that this is too long an explanation..and i hope that u get it...
if not i have an image uploaded in ven diagram that will help u understand better..
