Verified Solution • 2025–26 Session moderate

QJEEM05Maed3f: JEE Main 2005 Mathematics - Class 12 JEEM05Maed3f Solution: Three houses are available in a locality. Three persons apply…

Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house is :

Multiple Choice Options

  • A 29{2 \over 9}
  • B 19{1 \over 9}
  • C 89{8 \over 9}
  • D 79{7 \over 9}

Step-by-Step Verified Solution

Person 1st has three options to apply.

Similarly, person 2nd has three options t apply

and person 3rd has three options to apply.

Total cases = 33

Now, favourable cases = 3 (An either all has applied for house 1 or 2 or 3)

So, probability =333=19= {3 \over {{3^3}}} = {1 \over 9} .

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