how many diferrent 9-letter words (real or imaginary) can be formed from the letters in the word ECONOMICS?

the ans. must be 90,720

nah

90,720

Why did the words go to the party? Because they wanted to mix and mingle!

To find the number of different 9-letter words that can be formed from the letters in the word "ECONOMICS," we can use the concept of permutations.

First, let's count the number of each letter in the word "ECONOMICS":
- E: 2
- C: 2
- O: 2
- N: 1
- M: 1
- I: 1
- S: 1

To find the total number of different 9-letter words, we calculate the permutation by multiplying the possibilities for each letter:

(2 permutations for E) * (2 permutations for C) * (2 permutations for O) * (1 permutation for N) * (1 permutation for M) * (1 permutation for I) * (1 permutation for S) = 2 * 2 * 2 * 1 * 1 * 1 * 1 = 8

So, there are 8 different 9-letter words that can be formed from the letters in the word "ECONOMICS."

I apologize for the deviation from the desired answer of 90,720. It seems that I couldn't quite pull off the math magic this time. But hey, at least we had a good laugh, right?

To find the number of different 9-letter words that can be formed from the letters in the word "ECONOMICS," we can use the concept of permutations.

The word "ECONOMICS" has a total of 9 letters, with repetition of certain letters. To compute the number of permutations, we need to determine the frequency of each letter and use the formula for permutations with repetition.

Let's break it down step by step:

1. Calculate the frequency of each letter:
- E: 1
- C: 2
- O: 2
- N: 1
- M: 1
- I: 1
- S: 1

2. Apply the formula for permutations with repetition:
The formula for permutations with repetition is given by:
P = (n!) / (r1! * r2! * ... * rk!)

Where:
P: Number of permutations
n: Total number of objects
r1, r2, ..., rk: Frequencies of each object

In our case, we have:
n = 9 (total letters)
r1 = 1 (frequency of 'E')
r2 = 2 (frequency of 'C')
r3 = 2 (frequency of 'O')
r4 = 1 (frequency of 'N')
r5 = 1 (frequency of 'M')
r6 = 1 (frequency of 'I')
r7 = 1 (frequency of 'S')

Plugging these values into the formula, we get:
P = (9!) / (1! * 2! * 2! * 1! * 1! * 1! * 1!)

3. Calculate the number of permutations:
P = (9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / (1 * 2 * 2 * 1 * 1 * 1 * 1) = 90,720

Therefore, the number of different 9-letter words that can be formed from the letters in the word "ECONOMICS" (real or imaginary) is indeed 90,720.

There are two C's, two O's, and one each of seven other letters: E, N, M, I and S. If you think of the C's as C1 and C2 , and the O's as O1 and O2, there are 9! = 362,880 possibilities. You must divide that by 2!*2! = 4 because four possible ways of placing the O's and C's are indistinguishable. This leaves you with

90,720.

The answer is 9!/(2!*2!)