# Find the number of different arrangements of letters in the word MAHARASHTRA. How many of these arrangements have letters M and T never together? - Mathematics and Statistics

Sum

Find the number of different arrangements of letters in the word MAHARASHTRA. How many of these arrangements have letters M and T never together?

#### Solution

Total number of letters in the word MAHARASHTRA = 11
The letter ‘A’ is repeated ‘4’ times.
The letter ‘H’ is repeated twice.
The letter ‘R’ is repeated twice.

∴ Number of arrangements = (11!)/(4!2!2!)

Other than M and T. there are 9 letters in which A repeats 4 times, H repeats twice, R repeats twice
The number of arrangements of the letter = (9!)/(4!2!2!)
These 9 letters create 10 gaps in which M and T are to be arranged
The number of the arrangement of M and T = 10P2
∴ Total number arrangement having M and T never together = (9!xx^10"P"_2)/(4!2!2!)

Concept: Permutations When All Objects Are Not Distinct
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#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 6 Permutations and Combinations
Exercise 6.4 | Q 6. (a) | Page 82