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One 5 letter ...

Question

One 5 letter word is to be formed taking all letters S, A, P, T and E. What is the probability that this the word formed will contain all vowels together?

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Solution

Total no. of words which can be formed = $5!$
Total no. of words in which vowel are together = $4! \times 2!$
So, Probablity that word formed will contain all vowels together = $\frac{2}{5}$

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