Find the number of arrangements of the letters of the word INDEPENDENCE. How many of these start with P.

Explanation

Total number of letters = 12.
N appears 3 times, E 4 times and D 2 times
`therefore` Number of arrangements `=(12!)/(3!4!2!)=1663200`
To find number of words starting with P.
fix P at the exteme left position
`therefore` remaining letters = 11
`therefore` Number of arrangements `= (11!)/(3!4!2!)=138600`