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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
If three letters can be posted to any one of the $5$ different addresses, then the probability that the three letters are posted to exactly two addresses is:
Solution
Total ways = each letter can go to any of 5 addresses$ = 5^3 = 125 $
Favourable cases (exactly two addresses used):
Step 1: Choose 2 addresses out of 5
$ = \binom{5}{2} = 10 $
Step 2: Distribute 3 letters among these 2 addresses such that both are used
Total ways to assign = $ 2^3 = 8 $
Subtract cases where all letters go to one address
$ = 2 $
So valid distributions
$ = 8 - 2 = 6 $
Total favourable
$ = 10 \times 6 = 60 $
Probability
$ = \frac{60}{125} = \frac{12}{25} $
Final Answer: $ \boxed{\frac{12}{25}} $
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