Given as
The word ‘MADHUBANI’
The total number of letters = 9
A total number of arrangements of word MADHUBANI excluding I: Total letters 8. Repeating letter A, repeating twice.
Total number of arrangements 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’, here's 7 places for 7 letters.
Total number of arrangements that start with ‘M’ and end with letter I = 7! / 2!
= [7 × 6 × 5 × 4 × 3 × 2!] / 2!
= 7 × 6 × 5 × 4 × 3
= 2520
Total number of arrangements that do not start with ‘M’ but end with letter I = The total number of arrangements that end with letter I – The total number of arrangements that start with ‘M’ and end with letter I
= 20160 – 2520
= 17640
Thus, a total number of arrangements of word MADHUBANI in such a way that the word is not starting with M but ends with I is 17640.
