Counting - Set Problem

[iikarthik]

If a town,16 people own Fords and 11 People own Toyotas.If exactly 15 people own only one type of two types of cars.how many people own both types of cars?

Soultion is : 6

I tried with the P(AUB) = P(Ford cars) + p(toyota cars) - P(Ford and Toyota)

15=16+11-P(Ford and Toyota)

P(Ford and Toyota)=12.

i dunno wats is wrong with my solution.

pls clarify

[ontopofit]

here 15 is the number of ppl with either one of the two cars so P(AUB) is not 15 , rather it is 15 + P(both A and B).....equate this and get the answer as 6.

[sureshbala]

Let x be the number of people who own both.

Hence people who own only Ford = 16-x and only Toyota = 11-x

Given (16-x)+(11-x)=15

So x =6

[iikarthik]

hi,

Thanks for ur reply.

But i still dont understand what went erong.

karthik

[bmlaud]

Solve this problem in a other way

n(F) = 16
n(t) = 11
n(FUT) = ??
n(F int T) = ??
n(FUT) - n(F int T) = 15 given.....1

also n(FUT) = n(F) + n(T) - n(F int T)
= 16+11- n(F int T) ....2

solve 1 and 2 n(FUT) = 21 and n(F int T) = 6

[x2suresh]

hi,

Thanks for ur reply.

But i still dont understand what went erong.

karthik

Think this way.


16 Fords owned by 16 People
11 Toyotaq owned by 11 people
15 people owned only one vehicle.

16+11 -15= 12 vehicles owned by "no. people who owned 2 vehicles each"

obviously only 6 person can own 12 vehicles.
If 12 persons then they should own 24 vehicles.