There are four letters and four envelopes and exactly one letter is to be put in exactly one envelope with the correct address. If the letters are randomly inserted into the envelopes, then consider the following statements:
1 It is possible that exactly one letter goes into an incorrect envelope.
2. There are only six ways in which only two letters can go into the correct envelopes.
Which of the statements given above is/are correct ?
This questions was previously asked in
Complete-Test, Previous year (2023)
Both 1 and 2
Incorrect AnswerNeither 1 nor 2
Incorrect AnswerExplanation:
- Statement 1: It's impossible for exactly one letter to be placed incorrectly if each envelope can only hold one letter. If one is correctly placed, all must be unless multiple swaps are possible.
- Statement 2: With four letters, checking for arrangements where exactly two are correctly placed involves combinations and permutations. There are exactly six ways to correctly achieve this condition.
- Option 1 ('1 only'): Incorrect because statement 1 is false.
- Option 2 ('2 only'): Correct as only statement 2 is true.
- Option 3 ('Both 1 and 2'): Incorrect since statement 1 is wrong.
- Option 4 ('Neither 1 nor 2'): Incorrect because statement 2 is true.
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By: sunny bhonsle