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The number of different words that can be formed using all the letters of the word 'SHASHANK' such that in any word the vowels are separated by atleast two consonants, is
 

Option: 1

2700


Option: 2

1800


Option: 3

900

 


Option: 4

600


Answers (1)

best_answer

1 The letters other than vowels are SHSHNK which can be arranged in \frac{6 !}{2 ! 2 !} ways.
Now in its each case, let the firstA be placed in the r^{\text {th }}gap. Then the number of ways to place the 2 nd A will be (7-r-1). So the total number of ways= 

\begin{aligned}& \frac{6 !}{2 ! 2 !} \sum_{r=1}^5(6-r)\\ & =\frac{6 !}{2 ! 2 !} \times(5+4+3+2+1) \\ & =2700 \end{aligned}

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shivangi.bhatnagar

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