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A person writes letters to six friends and addresses the corresponding envelopes. In how many ways can the letters be placed in the envelopes so that (i) all the letters are in the wrong envelopes. (ii) at least two of them are in the wrong envelopes?
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A person writes letters to six friends and addresses the corresponding...
Answer:


(i) All the letters are in the wrong envelopes


If all the letters are in the wrong envelopes, then each letter has 5 incorrect envelopes to go into. Therefore, the number of ways in which all the letters can be placed in the wrong envelopes is:


5 × 5 × 5 × 5 × 5 × 5 = 56 = 15625


(ii) At least two of them are in the wrong envelopes


To find the number of ways in which at least two letters are in the wrong envelopes, we can use the principle of inclusion-exclusion:



  • Number of ways in which no letters are in the wrong envelopes = 1

  • Number of ways in which exactly one letter is in the wrong envelope = 6 × 55 = 187500

  • Number of ways in which exactly two letters are in the wrong envelopes = (6C2 × 44) = 54000



Therefore, the number of ways in which at least two letters are in the wrong envelopes is:


1 + 187500 - 54000 = 133501
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A person writes letters to six friends and addresses the corresponding...
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A person writes letters to six friends and addresses the corresponding envelopes. In how many ways can the letters be placed in the envelopes so that (i) all the letters are in the wrong envelopes. (ii) at least two of them are in the wrong envelopes?
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A person writes letters to six friends and addresses the corresponding envelopes. In how many ways can the letters be placed in the envelopes so that (i) all the letters are in the wrong envelopes. (ii) at least two of them are in the wrong envelopes? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A person writes letters to six friends and addresses the corresponding envelopes. In how many ways can the letters be placed in the envelopes so that (i) all the letters are in the wrong envelopes. (ii) at least two of them are in the wrong envelopes? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A person writes letters to six friends and addresses the corresponding envelopes. In how many ways can the letters be placed in the envelopes so that (i) all the letters are in the wrong envelopes. (ii) at least two of them are in the wrong envelopes?.
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