This tool lists out all the arrangements possible using letters of a word under various conditions. This can be used to verify answers of the questions related to calculation of the number of arrangements using letters of a word.
This tool programmatically generates all the arrangements possible. If you want to find out the number of arrangements mathematically, use Permutations Calculator
For example, consider the following question.
How many words with or without meaning can be formed using the letters of 'CRICKET' such that all the vowels must come together?
The answer of the above problem is $720$. Using this tool, it is possible to generate all these $720$ arrangements programmatically.
At the same time, Permutations Calculator can be used for a mathematical solution to this problem as provided below.
The word 'CRICKET' has $7$ letters where $2$ are vowels (I, E). Vowels must come together. Therefore, group these vowels and consider it as a single letter. i.e., CRCKT, (IE) Thus we have total $6$ letters where C occurs $2$ times. Number of ways to arrange these $6$ letters $=6!2!=360$ All the $2$ vowels are different. Number of ways to arrange these $2$ vowels among themselves $=2!=2$ Required number of ways
$=360×2=720$
Note: This tool uses JavaScript for generating the number of permutations and can be slow for large strings.
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Discussion
- In what ways the letters of the word "CRICKET" can be arranged to form the different new words so that the vowels always come together?
| A. |
| B. |
| C. |
| D. |
Answer : Option A
Explanation :
No answer description available for this question.
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Exercise :: Permutation and Combination - General Questions
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| 2. | In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together? | |||||||||
Answer: Option C Explanation:
The word 'LEADING' has 7 different letters. When the vowels EAI are always together, they can be supposed to form one letter. Then, we have to arrange the letters LNDG (EAI). Now, 5 (4 + 1 = 5) letters can be arranged in 5! = 120 ways. The vowels (EAI) can be arranged among themselves in 3! = 6 ways. Video Explanation: //youtu.be/WCEF3iW3H2c |
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Exercise :: Permutation and Combination - General Questions
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| 7. | How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated? |
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Answer: Option D Explanation:
Since each desired number is divisible by 5, so we must have 5 at the unit place. So, there is 1 way of doing it. The tens place can now be filled by any of the remaining 5 digits (2, 3, 6, 7, 9). So, there are 5 ways of filling the tens place. The hundreds place can now be filled by any of the remaining 4 digits. So, there are 4 ways of filling it. |
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Exercise :: Permutation and Combination - General Questions
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| 13. | In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together? | |||||||||||||||
Answer: Option C Explanation:
In the word 'MATHEMATICS', we treat the vowels AEAI as one letter. Thus, we have MTHMTCS (AEAI). Now, we have to arrange 8 letters, out of which M occurs twice, T occurs twice and the rest are different.
Now, AEAI has 4 letters in which A occurs 2 times and the rest are different.
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