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Micky has 10 different letters and 5 different envelopes with him. If he can only put one letter in an envelope, in how many ways can the letters be put in the envelopes?
  • a)
    5!
  • b)
    55
  • c)
    10C5 *5!
  • d)
    10C5 *55
  • e)
    510
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Micky has 10 different letters and 5 different envelopes with him. If ...
Given
  • Number of letters = 10
  • Number of envelopes = 5
To Find: Number of ways in which 5 letters can be put in 5 envelopes?
Approach
  1. We need to find the number of ways in which 5 different letters out of 10 available letters can be put in 5 different envelopes.
  2. Task-1: Selecting 5 letters out of 10 letters
    1. We need to select 5 letters out of 10 available letters that are to be put in the envelopes
  3. Task-2: Putting 5 different letters in 5 different envelopes
    1. We need to distribute 5 different letters in 5 different envelopes
  4. Number of ways = Task-1 * Task-2
Working Out
  1. Task-1: Selecting 5 letters out of 10 letters
    1. Number of ways to select 5 different letters out of 10 different letters = 10 C5……(1)
  • Task-2: Putting 5 selected letters in 5 different envelopes
    1. 1st letter has an option of being put in 5 envelopes
    2. 2nd letter has an option of being put in any of the remaining 4 envelopes
    3. …….
    4. ….
    5. 5th letter has an option of being put in only 1 remaining envelope.
    6. So, total ways in which 5 different letters can be put in 5 different envelopes = 5 *4*3*2*1 = 5!........(2)
  • Combining (1) and (2), we have
    1. Number of ways of putting 5 different letters out of 10 different letters in 5 different envelopes = 10C5 * 5!
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Most Upvoted Answer
Micky has 10 different letters and 5 different envelopes with him. If ...
Given
  • Number of letters = 10
  • Number of envelopes = 5
To Find: Number of ways in which 5 letters can be put in 5 envelopes?
Approach
  1. We need to find the number of ways in which 5 different letters out of 10 available letters can be put in 5 different envelopes.
  2. Task-1: Selecting 5 letters out of 10 letters
    1. We need to select 5 letters out of 10 available letters that are to be put in the envelopes
  3. Task-2: Putting 5 different letters in 5 different envelopes
    1. We need to distribute 5 different letters in 5 different envelopes
  4. Number of ways = Task-1 * Task-2
Working Out
  1. Task-1: Selecting 5 letters out of 10 letters
    1. Number of ways to select 5 different letters out of 10 different letters = 10 C5……(1)
  • Task-2: Putting 5 selected letters in 5 different envelopes
    1. 1st letter has an option of being put in 5 envelopes
    2. 2nd letter has an option of being put in any of the remaining 4 envelopes
    3. …….
    4. ….
    5. 5th letter has an option of being put in only 1 remaining envelope.
    6. So, total ways in which 5 different letters can be put in 5 different envelopes = 5 *4*3*2*1 = 5!........(2)
  • Combining (1) and (2), we have
    1. Number of ways of putting 5 different letters out of 10 different letters in 5 different envelopes = 10C5 * 5!
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Community Answer
Micky has 10 different letters and 5 different envelopes with him. If ...
Given
  • Number of letters = 10
  • Number of envelopes = 5
To Find: Number of ways in which 5 letters can be put in 5 envelopes?
Approach
  1. We need to find the number of ways in which 5 different letters out of 10 available letters can be put in 5 different envelopes.
  2. Task-1: Selecting 5 letters out of 10 letters
    1. We need to select 5 letters out of 10 available letters that are to be put in the envelopes
  3. Task-2: Putting 5 different letters in 5 different envelopes
    1. We need to distribute 5 different letters in 5 different envelopes
  4. Number of ways = Task-1 * Task-2
Working Out
  1. Task-1: Selecting 5 letters out of 10 letters
    1. Number of ways to select 5 different letters out of 10 different letters = 10 C5……(1)
  • Task-2: Putting 5 selected letters in 5 different envelopes
    1. 1st letter has an option of being put in 5 envelopes
    2. 2nd letter has an option of being put in any of the remaining 4 envelopes
    3. …….
    4. ….
    5. 5th letter has an option of being put in only 1 remaining envelope.
    6. So, total ways in which 5 different letters can be put in 5 different envelopes = 5 *4*3*2*1 = 5!........(2)
  • Combining (1) and (2), we have
    1. Number of ways of putting 5 different letters out of 10 different letters in 5 different envelopes = 10C5 * 5!
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Micky has 10 different letters and 5 different envelopes with him. If he can only put one letter in an envelope, in how many ways can the letters be put in the envelopes?a)5!b)55c)10C5 *5!d)10C5 *55e)510Correct answer is option 'C'. Can you explain this answer?
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Micky has 10 different letters and 5 different envelopes with him. If he can only put one letter in an envelope, in how many ways can the letters be put in the envelopes?a)5!b)55c)10C5 *5!d)10C5 *55e)510Correct answer is option 'C'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Micky has 10 different letters and 5 different envelopes with him. If he can only put one letter in an envelope, in how many ways can the letters be put in the envelopes?a)5!b)55c)10C5 *5!d)10C5 *55e)510Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Micky has 10 different letters and 5 different envelopes with him. If he can only put one letter in an envelope, in how many ways can the letters be put in the envelopes?a)5!b)55c)10C5 *5!d)10C5 *55e)510Correct answer is option 'C'. Can you explain this answer?.
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