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The letters of the words CALCUTTA and AMERICA are arranged in all possible ways.The ratio of the number of there arrangements is
- a)1 : 2
- b)2 : 1
- c)2 : 2
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The letters of the words CALCUTTA and AMERICA are arranged in all poss...
We are asked to find the ratio of the number of arrangements of the letters of the words "CALCUTTA" and "AMERICA."
Step 1: Number of Arrangements of CALCUTTA
The word "CALCUTTA" consists of 8 letters in total: C, A, L, C, U, T, T, A.
The repeated letters are:
The word "CALCUTTA" consists of 8 letters in total: C, A, L, C, U, T, T, A.
The repeated letters are:
- "C" appears 2 times,
- "A" appears 2 times,
- "T" appears 2 times.
The number of distinct arrangements of the letters of "CALCUTTA" is given by the formula for permutations of a multiset:
Arrangements of CALCUTTA = π / (2! × 2! × 2!)
Arrangements of CALCUTTA = π / (2! × 2! × 2!)
Calculating:
Arrangements of CALCUTTA = (8!) / (2! × 2! × 2!) = 40320 / 8 = 5040
Arrangements of CALCUTTA = (8!) / (2! × 2! × 2!) = 40320 / 8 = 5040
Step 2: Number of Arrangements of AMERICA
The word "AMERICA" consists of 7 letters: A, M, E, R, I, C, A.
The letter "A" repeats 2 times.
The number of distinct arrangements of the letters of "AMERICA" is:
Arrangements of AMERICA = π / (2!)
The word "AMERICA" consists of 7 letters: A, M, E, R, I, C, A.
The letter "A" repeats 2 times.
The number of distinct arrangements of the letters of "AMERICA" is:
Arrangements of AMERICA = π / (2!)
Calculating:
Arrangements of AMERICA = (7!) / (2!) = 5040 / 2 = 2520
Arrangements of AMERICA = (7!) / (2!) = 5040 / 2 = 2520
Step 3: Finding the Ratio
The ratio of the number of arrangements of "CALCUTTA" to "AMERICA" is:
Ratio = (5040) / (2520) = 2:1
Thus, the ratio of the number of arrangements is 2 : 1.
The ratio of the number of arrangements of "CALCUTTA" to "AMERICA" is:
Ratio = (5040) / (2520) = 2:1
Thus, the ratio of the number of arrangements is 2 : 1.
Most Upvoted Answer
The letters of the words CALCUTTA and AMERICA are arranged in all poss...
Arrangements of CALCUTTA:
- The word CALCUTTA has 8 letters.
- The number of ways to arrange 8 letters is 8! = 40,320.
Arrangements of AMERICA:
- The word AMERICA has 7 letters.
- The number of ways to arrange 7 letters is 7! = 5,040.
Ratio of arrangements:
- The ratio of the number of arrangements of CALCUTTA to AMERICA is 40,320/5,040 = 8/1.
- Simplifying the ratio gives 2/1.
Therefore, the correct answer is option B) 2 : 1.
- The word CALCUTTA has 8 letters.
- The number of ways to arrange 8 letters is 8! = 40,320.
Arrangements of AMERICA:
- The word AMERICA has 7 letters.
- The number of ways to arrange 7 letters is 7! = 5,040.
Ratio of arrangements:
- The ratio of the number of arrangements of CALCUTTA to AMERICA is 40,320/5,040 = 8/1.
- Simplifying the ratio gives 2/1.
Therefore, the correct answer is option B) 2 : 1.
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Community Answer
The letters of the words CALCUTTA and AMERICA are arranged in all poss...
The given words are CALCUTTA and AMERICA.
Total number of letters in CALCUTTA = 8
Total number of letters in AMERICA = 7
Therefore, the total number of arrangements possible for CALCUTTA and AMERICA can be calculated as follows:
Number of arrangements for CALCUTTA = 8!
Number of arrangements for AMERICA = 7!
To find the ratio of the number of arrangements, we can simply divide the two values:
Ratio = (8!)/(7!) = 8
Therefore, the ratio of the number of arrangements of CALCUTTA to AMERICA is 8:1, which means that for every 8 arrangements of CALCUTTA, there is only 1 arrangement of AMERICA.
Hence, the correct answer is option B, 2:1.
Total number of letters in CALCUTTA = 8
Total number of letters in AMERICA = 7
Therefore, the total number of arrangements possible for CALCUTTA and AMERICA can be calculated as follows:
Number of arrangements for CALCUTTA = 8!
Number of arrangements for AMERICA = 7!
To find the ratio of the number of arrangements, we can simply divide the two values:
Ratio = (8!)/(7!) = 8
Therefore, the ratio of the number of arrangements of CALCUTTA to AMERICA is 8:1, which means that for every 8 arrangements of CALCUTTA, there is only 1 arrangement of AMERICA.
Hence, the correct answer is option B, 2:1.
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The letters of the words CALCUTTA and AMERICA are arranged in all possible ways.The ratio of the number of there arrangements isa)1 : 2b)2 : 1c)2 : 2d)none of theseCorrect answer is option 'B'. Can you explain this answer? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The letters of the words CALCUTTA and AMERICA are arranged in all possible ways.The ratio of the number of there arrangements isa)1 : 2b)2 : 1c)2 : 2d)none of theseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The letters of the words CALCUTTA and AMERICA are arranged in all possible ways.The ratio of the number of there arrangements isa)1 : 2b)2 : 1c)2 : 2d)none of theseCorrect answer is option 'B'. Can you explain this answer?.
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