How many different ways can the letters in the word COMBINATIONS be arranged if the letter C is first and the letter S is last?
Thank you in advance ^^
Since the first and last are fixed, that leaves you with the letters
OMBINATION , I see two I's and two O's
number of arrangements of these
= 10!/(2!2!) = 907200
To find the number of different ways the letters in the word "COMBINATIONS" can be arranged, given that the letter C is first and the letter S is last, we can follow these steps:
Step 1: Count the number of total letters.
In the word "COMBINATIONS," there are 12 letters.
Step 2: Subtract 1 from the total number of letters.
Since the letter C is fixed as the first letter, we subtract 1 from 12.
12 - 1 = 11.
Step 3: Subtract 1 from the result obtained in Step 2.
Since the letter S is fixed as the last letter, we subtract 1 from 11.
11 - 1 = 10.
Step 4: Calculate the factorial of the number obtained in Step 3.
To find the number of arrangements, we calculate the factorial of 10.
Factorial of 10 = 10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3,628,800.
Therefore, there are 3,628,800 different ways the letters in the word "COMBINATIONS" can be arranged with C as the first letter and S as the last letter.