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In how many different ways can the letters of the name ‘ASHWATHAMA’ be arranged such that the letter ‘S’ always comes with the letter ‘T’.

In how many different ways can the letters of the name ‘ASHWATHAMA’ be arranged such that the letter ‘S’ always comes with the letter ‘T’. Correct Answer 15120 ways

Concept:

The word ‘ASHWATHAMA’ has 10 letters. Letter ‘S’ and ‘T’ always come together. Hence these 2 letters can be grouped and considered as a single letter. So, we can assume total letters as 9. And if a letter occurs more than once in a word,

we divide the factorial of the numbers of all letters in the word by the number of occurrences of each letter.

Calculation:

In these 9 letters (‘S’ and ‘T’ in a single group) ‘A’ occurs 4 times and ‘H’ occurs 2 times.

Number of ways to arrange these letters = 9!/(4! × 2!)

And also letter ‘S’ and ‘T’ can change their position by 2! ways

∴ Number of ways to arrange these letters such that ‘S’ and ‘T’ comes together = 9! × 2!/(4! × 2!) = 9 × 8 × 7 × 6 × 5 = 15,120

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