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A string of three English letters is formed as per the following rules :
(a) The first letter is any vowel.
(b) The second letter is m, n or p.
(c) If the second letter is m then the third letter is any vowel which is different from the first letter.
(d) If the second letter is n then the third letter is e or u.
(e) If the second letter is p then the third letter is the same as the first letter.
(a) The first letter is any vowel.
(b) The second letter is m, n or p.
(c) If the second letter is m then the third letter is any vowel which is different from the first letter.
(d) If the second letter is n then the third letter is e or u.
(e) If the second letter is p then the third letter is the same as the first letter.
Q. How many strings of letters can possibly be formed using the above rules ?
- a)40
- b)45
- c)30
- d)35
Correct answer is option 'D'. Can you explain this answer?
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A string of three English letters is formed as per the following rules...
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A string of three English letters is formed as per the following rules...
To solve this problem, we need to go through each rule and determine the possible choices for each letter. Let's analyze each rule one by one:
(a) The first letter is any vowel.
There are 5 vowels in the English alphabet - a, e, i, o, and u. So, there are 5 choices for the first letter.
(b) The second letter is m, n, or p.
There are 3 choices for the second letter - m, n, or p.
(c) If the second letter is m, then the third letter is any vowel different from the first letter.
If the second letter is m, we have already used one vowel as the first letter. So, we have 4 remaining vowels to choose from for the third letter. Therefore, if the second letter is m, there are 4 choices for the third letter.
(d) If the second letter is n, then the third letter is e or u.
If the second letter is n, there are 2 choices for the third letter - e or u.
(e) If the second letter is p, then the third letter is the same as the first letter.
If the second letter is p, we have already chosen a vowel as the first letter. So, there is only 1 choice for the third letter, which is the same as the first letter.
Now, let's combine the choices for each letter based on the rules:
- If the second letter is m:
- First letter: 5 choices (a, e, i, o, or u)
- Second letter: 1 choice (m)
- Third letter: 4 choices (any vowel different from the first letter)
Total choices: 5 * 1 * 4 = 20
- If the second letter is n:
- First letter: 5 choices (a, e, i, o, or u)
- Second letter: 1 choice (n)
- Third letter: 2 choices (e or u)
Total choices: 5 * 1 * 2 = 10
- If the second letter is p:
- First letter: 5 choices (a, e, i, o, or u)
- Second letter: 1 choice (p)
- Third letter: 1 choice (same as the first letter)
Total choices: 5 * 1 * 1 = 5
Now, add up the total choices from each case:
Total choices = 20 + 10 + 5 = 35
Therefore, the correct answer is option (d) 35.
(a) The first letter is any vowel.
There are 5 vowels in the English alphabet - a, e, i, o, and u. So, there are 5 choices for the first letter.
(b) The second letter is m, n, or p.
There are 3 choices for the second letter - m, n, or p.
(c) If the second letter is m, then the third letter is any vowel different from the first letter.
If the second letter is m, we have already used one vowel as the first letter. So, we have 4 remaining vowels to choose from for the third letter. Therefore, if the second letter is m, there are 4 choices for the third letter.
(d) If the second letter is n, then the third letter is e or u.
If the second letter is n, there are 2 choices for the third letter - e or u.
(e) If the second letter is p, then the third letter is the same as the first letter.
If the second letter is p, we have already chosen a vowel as the first letter. So, there is only 1 choice for the third letter, which is the same as the first letter.
Now, let's combine the choices for each letter based on the rules:
- If the second letter is m:
- First letter: 5 choices (a, e, i, o, or u)
- Second letter: 1 choice (m)
- Third letter: 4 choices (any vowel different from the first letter)
Total choices: 5 * 1 * 4 = 20
- If the second letter is n:
- First letter: 5 choices (a, e, i, o, or u)
- Second letter: 1 choice (n)
- Third letter: 2 choices (e or u)
Total choices: 5 * 1 * 2 = 10
- If the second letter is p:
- First letter: 5 choices (a, e, i, o, or u)
- Second letter: 1 choice (p)
- Third letter: 1 choice (same as the first letter)
Total choices: 5 * 1 * 1 = 5
Now, add up the total choices from each case:
Total choices = 20 + 10 + 5 = 35
Therefore, the correct answer is option (d) 35.
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A string of three English letters is formed as per the following rules :(a) The first letter is any vowel.(b) The second letter is m, n or p.(c) If the second letter is m then the third letter is any vowel which is different from the first letter.(d) If the second letter is n then the third letter is e or u.(e) If the second letter is p then the third letter is the same as the first letter.Q.How many strings of letters can possibly be formed using the above rules ?a)40b)45c)30d)35Correct answer is option 'D'. Can you explain this answer?
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A string of three English letters is formed as per the following rules :(a) The first letter is any vowel.(b) The second letter is m, n or p.(c) If the second letter is m then the third letter is any vowel which is different from the first letter.(d) If the second letter is n then the third letter is e or u.(e) If the second letter is p then the third letter is the same as the first letter.Q.How many strings of letters can possibly be formed using the above rules ?a)40b)45c)30d)35Correct answer is option 'D'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A string of three English letters is formed as per the following rules :(a) The first letter is any vowel.(b) The second letter is m, n or p.(c) If the second letter is m then the third letter is any vowel which is different from the first letter.(d) If the second letter is n then the third letter is e or u.(e) If the second letter is p then the third letter is the same as the first letter.Q.How many strings of letters can possibly be formed using the above rules ?a)40b)45c)30d)35Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A string of three English letters is formed as per the following rules :(a) The first letter is any vowel.(b) The second letter is m, n or p.(c) If the second letter is m then the third letter is any vowel which is different from the first letter.(d) If the second letter is n then the third letter is e or u.(e) If the second letter is p then the third letter is the same as the first letter.Q.How many strings of letters can possibly be formed using the above rules ?a)40b)45c)30d)35Correct answer is option 'D'. Can you explain this answer?.
A string of three English letters is formed as per the following rules :(a) The first letter is any vowel.(b) The second letter is m, n or p.(c) If the second letter is m then the third letter is any vowel which is different from the first letter.(d) If the second letter is n then the third letter is e or u.(e) If the second letter is p then the third letter is the same as the first letter.Q.How many strings of letters can possibly be formed using the above rules ?a)40b)45c)30d)35Correct answer is option 'D'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A string of three English letters is formed as per the following rules :(a) The first letter is any vowel.(b) The second letter is m, n or p.(c) If the second letter is m then the third letter is any vowel which is different from the first letter.(d) If the second letter is n then the third letter is e or u.(e) If the second letter is p then the third letter is the same as the first letter.Q.How many strings of letters can possibly be formed using the above rules ?a)40b)45c)30d)35Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A string of three English letters is formed as per the following rules :(a) The first letter is any vowel.(b) The second letter is m, n or p.(c) If the second letter is m then the third letter is any vowel which is different from the first letter.(d) If the second letter is n then the third letter is e or u.(e) If the second letter is p then the third letter is the same as the first letter.Q.How many strings of letters can possibly be formed using the above rules ?a)40b)45c)30d)35Correct answer is option 'D'. Can you explain this answer?.
Solutions for A string of three English letters is formed as per the following rules :(a) The first letter is any vowel.(b) The second letter is m, n or p.(c) If the second letter is m then the third letter is any vowel which is different from the first letter.(d) If the second letter is n then the third letter is e or u.(e) If the second letter is p then the third letter is the same as the first letter.Q.How many strings of letters can possibly be formed using the above rules ?a)40b)45c)30d)35Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for UPSC.
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A string of three English letters is formed as per the following rules :(a) The first letter is any vowel.(b) The second letter is m, n or p.(c) If the second letter is m then the third letter is any vowel which is different from the first letter.(d) If the second letter is n then the third letter is e or u.(e) If the second letter is p then the third letter is the same as the first letter.Q.How many strings of letters can possibly be formed using the above rules ?a)40b)45c)30d)35Correct answer is option 'D'. Can you explain this answer?, a detailed solution for A string of three English letters is formed as per the following rules :(a) The first letter is any vowel.(b) The second letter is m, n or p.(c) If the second letter is m then the third letter is any vowel which is different from the first letter.(d) If the second letter is n then the third letter is e or u.(e) If the second letter is p then the third letter is the same as the first letter.Q.How many strings of letters can possibly be formed using the above rules ?a)40b)45c)30d)35Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of A string of three English letters is formed as per the following rules :(a) The first letter is any vowel.(b) The second letter is m, n or p.(c) If the second letter is m then the third letter is any vowel which is different from the first letter.(d) If the second letter is n then the third letter is e or u.(e) If the second letter is p then the third letter is the same as the first letter.Q.How many strings of letters can possibly be formed using the above rules ?a)40b)45c)30d)35Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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