Question

How many permutations can be formed from all the letters in the word engineering?

Answer 1

Answer:

277,200

Step-by-step explanation:

To find the number of permutation we can form from the letters of the word "engineering", we first need to find the frequencies of the different letters present.

E = 3

G = 2

N= 3

I = 2

R = 1

Now that we have the frequencies, we count the number of letters in the word "engineering".

E N G I N E E R I N G

11 letters

Now we take the factorial of total number of letters and divide it by the number of repeats and their factorial

So we get:

$\dfrac{11!}{3!2!3!2!1!}$

We remove the 1! because it will just yield 1.

$\dfrac{11!}{3!2!3!2!}$

So the total number of permutations from the letters of the word "engineering" will be:

Total number of permutations = $\dfrac{39,916,800}{144}$

Total number of permutations = 277,200