Question

Determine the number of distinguishable arrangement of the letters in the word APPROXIMATION

Answer 1

Solution:

The word ‘APPROXIMATION’ have 2 times A, 2 times P, 1 time R, 2 time O, 1 time X, 2 time I, 1 time M, 1 time T, and one time N.

A = 2

P = 2

R = 1

O = 2

X = 1

I = 2

M = 1

T = 1

N = 1

Total number of letters = n = 13

Since letters are repeating, so we have to use following formula:

Total number of arrangements = n!/p_i!

Total number of arrangements = 13!/(2!*2!*1!*2!*1!*2!*1!*1!*1!)

Total number of arrangements = 13!/(2!*2!*2!*2!)

Total number of arrangements = 13!/(2*2*2*2)

Total number of arrangements = 13!/16

Total number of arrangements = 6227020800 / 16

Total number of arrangements = 389188800