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Words, with or without meaning, are to be formed using all the letters of the word EXAMINATION. The probability that the letter M appears at the fourth position in any such word is
- a)1/9
- b)1/66
- c)2/11
- d)1/11
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Words, with or without meaning, are to be formed using all the letters...
AAEIIMNNOTX
Total words with M at fourth place =
Probability =
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Words, with or without meaning, are to be formed using all the letters...
Understanding the Problem
To find the probability that the letter M appears in the fourth position of the word "EXAMINATION", we first need to analyze the letters and their arrangements.
Letters in "EXAMINATION"
- The word "EXAMINATION" consists of 11 letters: E, X, A, M, I, N, A, T, I, O, N.
- The letter A appears twice, the letter I appears twice, and the letter N appears twice. The letter M appears once.
Total Arrangements of the Word
- The total number of distinct arrangements of the letters in "EXAMINATION" is calculated using the formula for permutations of multiset:
\[
\text{Total arrangements} = \frac{11!}{2! \times 2! \times 2!}
\]
Where:
- 11! accounts for the total letters.
- The denominators (2!) account for the repeated letters A, I, and N.
Calculating:
\[
= \frac{39916800}{8} = 4989600
\]
Arrangements with M in the Fourth Position
- When M is fixed in the fourth position, we are left with 10 letters: E, X, A, I, N, A, T, I, O, N.
- The total arrangements with M fixed is:
\[
\text{Arrangements with M} = \frac{10!}{2! \times 2! \times 2!}
\]
Calculating:
\[
= \frac{3628800}{8} = 453600
\]
Calculating the Probability
- The probability that M is in the fourth position is given by:
\[
P(M \text{ in 4th position}) = \frac{\text{Arrangements with M}}{\text{Total arrangements}} = \frac{453600}{4989600}
\]
Simplifying:
\[
= \frac{1}{11}
\]
Final Answer
Thus, the probability that the letter M appears at the fourth position in any arrangement of the word "EXAMINATION" is:
**Option D: 1/11**.
To find the probability that the letter M appears in the fourth position of the word "EXAMINATION", we first need to analyze the letters and their arrangements.
Letters in "EXAMINATION"
- The word "EXAMINATION" consists of 11 letters: E, X, A, M, I, N, A, T, I, O, N.
- The letter A appears twice, the letter I appears twice, and the letter N appears twice. The letter M appears once.
Total Arrangements of the Word
- The total number of distinct arrangements of the letters in "EXAMINATION" is calculated using the formula for permutations of multiset:
\[
\text{Total arrangements} = \frac{11!}{2! \times 2! \times 2!}
\]
Where:
- 11! accounts for the total letters.
- The denominators (2!) account for the repeated letters A, I, and N.
Calculating:
\[
= \frac{39916800}{8} = 4989600
\]
Arrangements with M in the Fourth Position
- When M is fixed in the fourth position, we are left with 10 letters: E, X, A, I, N, A, T, I, O, N.
- The total arrangements with M fixed is:
\[
\text{Arrangements with M} = \frac{10!}{2! \times 2! \times 2!}
\]
Calculating:
\[
= \frac{3628800}{8} = 453600
\]
Calculating the Probability
- The probability that M is in the fourth position is given by:
\[
P(M \text{ in 4th position}) = \frac{\text{Arrangements with M}}{\text{Total arrangements}} = \frac{453600}{4989600}
\]
Simplifying:
\[
= \frac{1}{11}
\]
Final Answer
Thus, the probability that the letter M appears at the fourth position in any arrangement of the word "EXAMINATION" is:
**Option D: 1/11**.
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Words, with or without meaning, are to be formed using all the letters of the word EXAMINATION. The probability that the letter M appears at the fourth position in any such word isa)1/9b)1/66c)2/11d)1/11Correct answer is option 'D'. Can you explain this answer?
Question Description
Words, with or without meaning, are to be formed using all the letters of the word EXAMINATION. The probability that the letter M appears at the fourth position in any such word isa)1/9b)1/66c)2/11d)1/11Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Words, with or without meaning, are to be formed using all the letters of the word EXAMINATION. The probability that the letter M appears at the fourth position in any such word isa)1/9b)1/66c)2/11d)1/11Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Words, with or without meaning, are to be formed using all the letters of the word EXAMINATION. The probability that the letter M appears at the fourth position in any such word isa)1/9b)1/66c)2/11d)1/11Correct answer is option 'D'. Can you explain this answer?.
Words, with or without meaning, are to be formed using all the letters of the word EXAMINATION. The probability that the letter M appears at the fourth position in any such word isa)1/9b)1/66c)2/11d)1/11Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Words, with or without meaning, are to be formed using all the letters of the word EXAMINATION. The probability that the letter M appears at the fourth position in any such word isa)1/9b)1/66c)2/11d)1/11Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Words, with or without meaning, are to be formed using all the letters of the word EXAMINATION. The probability that the letter M appears at the fourth position in any such word isa)1/9b)1/66c)2/11d)1/11Correct answer is option 'D'. Can you explain this answer?.
Solutions for Words, with or without meaning, are to be formed using all the letters of the word EXAMINATION. The probability that the letter M appears at the fourth position in any such word isa)1/9b)1/66c)2/11d)1/11Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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Here you can find the meaning of Words, with or without meaning, are to be formed using all the letters of the word EXAMINATION. The probability that the letter M appears at the fourth position in any such word isa)1/9b)1/66c)2/11d)1/11Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Words, with or without meaning, are to be formed using all the letters of the word EXAMINATION. The probability that the letter M appears at the fourth position in any such word isa)1/9b)1/66c)2/11d)1/11Correct answer is option 'D'. Can you explain this answer?, a detailed solution for Words, with or without meaning, are to be formed using all the letters of the word EXAMINATION. The probability that the letter M appears at the fourth position in any such word isa)1/9b)1/66c)2/11d)1/11Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of Words, with or without meaning, are to be formed using all the letters of the word EXAMINATION. The probability that the letter M appears at the fourth position in any such word isa)1/9b)1/66c)2/11d)1/11Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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