Question

In how many distinguishable ways can you arrange the letters in the word CONNECTICUT? *

Answer 1

Answer:

The number of distinguishable arrangements are 1,663,200.

Step-by-step explanation:

The word is: CONNECTICUT

The number of ways to arrange a word when no conditions are applied is:

$\frac{n!}{k_{1}!\cdot k_{2}!\cdot k_{3}!...\cdot k_{n}!}$

Here k is the number of times a word is repeated.

In the word CONNECTICUT there are:

3 Cs

2 Ns

2 Ts

And there are a total of n = 11 letters

So, the number of distinguishable arrangements are:

$\frac{n!}{k_{1}!\cdot k_{2}!\cdot k_{3}!...\cdot k_{n}!}=\frac{11!}{3!\times 2!\times 2!}$

                     $=\frac{39916800}{6\times 2\times 2}\\\\=1663200$

Thus, the number of distinguishable arrangements are 1,663,200.