Question -
Answer -
Given:
The word ‘MADHUBANI’
Total number ofletters = 9
A total number ofarrangements of word MADHUBANI excluding I: Total letters 8. Repeating letterA, repeating twice.
The total number ofarrangements that end with letter I = 8! / 2!
= [8×7×6×5×4×3×2!] /2!
= 8×7×6×5×4×3
= 20160
If the word start with‘M’ and end with ‘I’, there are 7 places for 7 letters.
The total number ofarrangements that start with ‘M’ and end with letter I = 7! / 2!
= [7×6×5×4×3×2!] / 2!
= 7×6×5×4×3
= 2520
The total number ofarrangements that do not start with ‘M’ but end with letter I = The totalnumber of arrangements that end with letter I – The total number ofarrangements that start with ‘M’ and end with letter I
= 20160 – 2520
= 17640
Hence, a total numberof arrangements of word MADHUBANI in such a way that the word is not startingwith M but ends with I is 17640.