Question

How many ways can the letters of the word organism be arranged so that the third letter is G

Answer 1

5040.

Explanation:

There are 7 letters other than G in the word organism and there are no repeats.

The number of ways 7 letters can be arranged = 7! and that is the answer,

7! = 5040.

Answer 2

5040

Explanation:

"organism" has 8 letters. Since the g is not to be permutated, let's take it out, and we're left with 7 letters.

For the first position we have 7 options. For the second position we have 6 options, etc., so 7*6*5*4*3*2*1 = 7! = 5040.

The "g" we just insert at the 3rd position, it doesn't play any role in the counting.