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If the letters of the word CRICKET are arranged in all possible ways and these words are written out as in the dictionary, then the rank of the word CRICKET is
- a)411
- b)529
- c)531
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
If the letters of the word CRICKET are arranged in all possible ways a...
The number of words starting with CC = 5! = 120
The number of words starting with CE = 5! = 120
The number of words starting with CI = 5! = 120
The number of words starting with CK = 5! = 120
The number of words starting with CRC = 4! = 24
The number of words starting with CRE = 4! = 24
The words starting with CRI are CRICEKT, CRICETK, then comes CRICKET automatically
So, the rank of cricket is 120 + 120 + 120 + 120 + 24 + 24 + 1 + 1 + 1 = 531
Therefore, the answer is 531.
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Community Answer
If the letters of the word CRICKET are arranged in all possible ways a...
The word "CRICKET" has 7 letters. In order to find the rank of the word in all possible arrangements, we need to consider the words that can be formed by rearranging the letters of "CRICKET" in alphabetical order.
Step 1: Arrange the letters of "CRICKET" in alphabetical order.
The letters in "CRICKET" arranged alphabetically are: CCEIKRT
Step 2: Find the number of words that can be formed starting with each letter.
Since the letters are arranged in alphabetical order, we can determine the number of words that can be formed starting with each letter by considering the remaining letters. In this case, we have:
- Words starting with C: The remaining letters are CEIKRT. The number of words that can be formed starting with C is (6!)/(2!1!1!) = 720/2 = 360.
- Words starting with E: The remaining letters are CIKRT. The number of words that can be formed starting with E is (5!)/(1!1!1!1!1!) = 120.
- Words starting with I: The remaining letters are CKRT. The number of words that can be formed starting with I is (4!)/(1!1!1!1!) = 24.
- Words starting with K: The remaining letters are CRT. The number of words that can be formed starting with K is (3!)/(1!1!1!) = 6.
- Words starting with R: The remaining letters are CTK. The number of words that can be formed starting with R is (3!)/(1!1!1!) = 6.
- Words starting with T: The remaining letters are CRK. The number of words that can be formed starting with T is (3!)/(1!1!1!) = 6.
Step 3: Determine the rank of the word "CRICKET".
To find the rank of the word "CRICKET", we need to consider the words that can be formed by rearranging the letters in alphabetical order. The rank of the word is obtained by summing up the number of words starting with each letter that comes before "CRICKET" in alphabetical order.
- Words starting with A: There are no words starting with A.
- Words starting with B: There are no words starting with B.
- Words starting with C: There are 360 words starting with C.
- Words starting with D: There are no words starting with D.
- Words starting with E: There are 120 words starting with E.
- Words starting with F: There are no words starting with F.
- Words starting with G: There are no words starting with G.
- Words starting with H: There are no words starting with H.
- Words starting with I: There are 24 words starting with I.
- Words starting with J: There are no words starting with J.
- Words starting with K: There are 6 words starting with K.
- Words starting with L: There are no words starting with L.
- Words starting with M: There are no words starting with M.
- Words starting with N: There are no words starting with N.
- Words starting with O: There are no words starting with O.
- Words starting with P: There are no words starting with P.
- Words starting with Q: There are
Step 1: Arrange the letters of "CRICKET" in alphabetical order.
The letters in "CRICKET" arranged alphabetically are: CCEIKRT
Step 2: Find the number of words that can be formed starting with each letter.
Since the letters are arranged in alphabetical order, we can determine the number of words that can be formed starting with each letter by considering the remaining letters. In this case, we have:
- Words starting with C: The remaining letters are CEIKRT. The number of words that can be formed starting with C is (6!)/(2!1!1!) = 720/2 = 360.
- Words starting with E: The remaining letters are CIKRT. The number of words that can be formed starting with E is (5!)/(1!1!1!1!1!) = 120.
- Words starting with I: The remaining letters are CKRT. The number of words that can be formed starting with I is (4!)/(1!1!1!1!) = 24.
- Words starting with K: The remaining letters are CRT. The number of words that can be formed starting with K is (3!)/(1!1!1!) = 6.
- Words starting with R: The remaining letters are CTK. The number of words that can be formed starting with R is (3!)/(1!1!1!) = 6.
- Words starting with T: The remaining letters are CRK. The number of words that can be formed starting with T is (3!)/(1!1!1!) = 6.
Step 3: Determine the rank of the word "CRICKET".
To find the rank of the word "CRICKET", we need to consider the words that can be formed by rearranging the letters in alphabetical order. The rank of the word is obtained by summing up the number of words starting with each letter that comes before "CRICKET" in alphabetical order.
- Words starting with A: There are no words starting with A.
- Words starting with B: There are no words starting with B.
- Words starting with C: There are 360 words starting with C.
- Words starting with D: There are no words starting with D.
- Words starting with E: There are 120 words starting with E.
- Words starting with F: There are no words starting with F.
- Words starting with G: There are no words starting with G.
- Words starting with H: There are no words starting with H.
- Words starting with I: There are 24 words starting with I.
- Words starting with J: There are no words starting with J.
- Words starting with K: There are 6 words starting with K.
- Words starting with L: There are no words starting with L.
- Words starting with M: There are no words starting with M.
- Words starting with N: There are no words starting with N.
- Words starting with O: There are no words starting with O.
- Words starting with P: There are no words starting with P.
- Words starting with Q: There are
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If the letters of the word CRICKET are arranged in all possible ways and these words are written out as in the dictionary, then the rank of the word CRICKET isa)411b)529c)531d)none of theseCorrect answer is option 'C'. Can you explain this answer?
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