Find the number of arrangements of the letters of the word INDEPENDENCE. In how many of these arrangements, do the word start with P?

Question

Find the number of arrangements of the letters of the word INDEPENDENCE. In how many of these arrangements, do the word start with P? (A)  1663200, 138600  (B)  1663000, 135600 (C)  1660000, 138650 (D) None of these

Tardigrade Admin · Accepted Answer

There are 12 letters, of which N appears 3 times, E appears 4 times and D appears 2 times and the rest all are different. Therefore, the required number of arrangements = (12!/3! 4! 2!) = 1663200. Let us fix P at the extreme left position, we then count the arrangements of the remaining 11 letters. Therefore, the required number of words starting with P are =(11!/ 3! 2! 4!)= 138600.

Q. Find the number of arrangements of the letters of the word INDEPENDENCE. In how many of these arrangements, do the word start with $P$ ?

$1663200, 138600$

$1663000, 135600$

$1660000, 138650$

None of these

Q. Find the number of arrangements of the letters of the word INDEPENDENCE. In how many of these arrangements, do the word start with P?

1663200,138600

1663000,135600

1660000,138650

None of these

Q. Find the number of arrangements of the letters of the word INDEPENDENCE. In how many of these arrangements, do the word start with $P$ ?

$1663200, 138600$

$1663000, 135600$

$1660000, 138650$