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

Answer 2

The total permutations which can be formed from all the letters in the word engineering is 277,200.

What is permutation?

The permutation is the arrangement of the things or object in a systematic order, in all the possible ways. The order of arrangement in permutation is in linear.

The given word is “ENGINEERING”. In this word there are total 11 letters in which,

• The letter E appears 3 times.
• The letter N appears 3 times.
• The letter G appears 2 times.
• The letter I appear 2 times.
• The letter R appears 1 time.

The number of permutation to arrange this letter is,

$nPr=\dfrac{11!}{(3!)(3!)(2!)(2!)(1!)}\\nPr=\dfrac{11\times10\times9\times8\times7\times6\times5\times4\times3!}{(3!)(3!)(2!)(2!)(1!)}\\nPr=277200$

Thus, the total permutations which can be formed from all the letters in the word engineering is 277,200.

Learn more about the permutations here;

https://brainly.com/question/12468032