Question

Find the number of different arrangement of letter in the word maharashtra how many of these arrangement have
a.Letters r and h never together
b.All vowels together?

Answer 1

Letters r and h never together = 10!/32 = 1,13,400  in arrangements of letter of Maharashtra , All vowels together = 10080

Step-by-step explanation:

maharashtra

M - 1

A = 4

H - 2

R - 2

S = 1

T -  1

Total = 11   Vowels = 4 Consonants = 7

Total Possible arrangement =  11! / ( 4!  * 2! * 2!)

= 11!/ 96

When r & h  are together

(r& h) - 1 Group  together in  2 Ways  rh  or hr

remaining are 9

9 + 1 = 10

Arrangements =  2 * 10! / 4!

= 10!/12

.Letters r and h never together =  11!/ 96  -  10!/12

= 10! (11  - 8)/96

= 10!/32

= 1,13,400

All vowels together AAAA  as 1 group

7 other

7 + 1 = 8

= 8! / (2! * 2 !)

= 2 * 7!

= 10080

Learn More :

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Answer 2

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