Question

Find the number of different arrangements of letters in the word MAHARASHTRA. How many of these arrangements have letters R and H never together?​

Answer 1

Answer:

R-2,H-2

In this word they never together.

Answer 2

Total number of different arrangements of letters in word MAHARASHTRA=415800

The number of different arrangements of letters in the word MAHARASHTRA  when R and H never comes together=113400

Step-by-step explanation:

Given word:MAHARASHTRA

Total number of letters=11

Number of R=2

Number of H=2

Number of A=4

Permutation:Total number of letters in a word =n

Letter t repeated r times and s repeated p times then the number of arrangements  of the word =$\frac{n!}{r!p!}$

By using the formula

Total number of different arrangements of letters in word MAHARASHTRA=$\frac{11!}{2!2!4!}=\frac{11\times 10\times 9\times 8\times 7\times 6\times 5\times 4!}{2\times 1\times 2\times 4!}=415800$

Total number of different arrangements of letters in word MAHARASHTRA=415800

When two letters R and H comes together

RH=I

Remaining letter except one R and one H=9

RH=One letter=I

Total number of letters=9+1=10

Number of ways in which R  and H can be arranged=2!

Number of arrangements of letters when R and H comes together=$\frac{10!}{4!}\times 2!=\frac{10\times 9\times 8\times 7\times 6\times 5\times 4!}{4!}\times 2\times 1=302400$

The number of different arrangements of letters in the word MAHARASHTRA  when R and H never comes together=$415800-302400=113400$

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