# Given TECHNOLOGY , find number of distinguishable ways the letters can be arranged in which letters T,E and N are together [closed]

Given TECHNOLOGY , find number of distinguishable ways the letters can be arranged in which letters T,E and N are together

This is my working-

$$3! \cdot \frac{7!}{2!}$$

is this correct ?

## closed as off-topic by Don Thousand, MisterRiemann, NCh, Shailesh, John BDec 1 '18 at 0:45

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• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Don Thousand, MisterRiemann, NCh, Shailesh
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• Solutions to such exercises should usually be presented in such a way that one can understand how you reached the answer, i.e. you should explain how you got that particular number, instead of just presenting the final answer. – MisterRiemann Nov 24 '18 at 15:00
• Be careful. TECHNOLOGY has ten letters, so you have a block of three letters and seven other letters to arrange. – N. F. Taussig Nov 24 '18 at 15:04

Assume $$T,E, N$$ as single letter therefore, total number of letters in the word technology is 8 this can be arranged in $$8!$$ ways and number of ways in which $$T,E, N$$ can be arranged $$3!$$ ways and since $$O$$ is repeating two times hence answer is $$\frac{8!×3!}{2!}$$.

Consider $$\text{TEN}$$ together as a block and all other letters as single block. Then you have $$8$$ blocks. So there are $$8!$$ permutations possible and $$3!$$ permutations of $$TEN$$. Also the letter $$\text{O}$$ is not distinguishable.
So total number of ways is $$\dfrac{8!\cdot 3!}{2!}$$.