Number of different words with the given conditions

To find the number of different words that can be formed using all the letters of the word BUTTERSCOTVH, with the word BUTTER always squeezed between two Cs, we need to follow the given rules. Let's break down the problem and solve it step by step.

Step 1: Identify the given word

The given word is BUTTERSCOTVH.

Step 2: Identify the word to be squeezed between two Cs

The word that needs to be squeezed between two Cs is BUTTER.

Step 3: Analyze the letters in the given word

The given word BUTTERSCOTVH has the following letters:
- B: 1
- U: 1
- T: 2
- E: 1
- R: 1
- S: 1
- C: 1
- O: 1
- V: 1
- H: 1

Step 4: Determine the number of ways to arrange the letters

To determine the number of different words that can be formed, we need to consider the arrangements of the letters. However, we need to ensure that the word BUTTER is always squeezed between two Cs.

Step 5: Determine the number of ways to arrange the remaining letters

Since the word BUTTER is fixed, we can remove those letters from consideration. Therefore, we are left with the following letters:
- B: 0
- U: 0
- T: 0
- E: 0
- R: 0
- S: 1
- C: 0
- O: 1
- V: 1
- H: 1

Step 6: Determine the number of ways to arrange the Cs

Since the word BUTTER is always squeezed between two Cs, we need to consider the arrangement of the Cs.

Step 7: Calculate the total number of different words

To calculate the total number of different words, we need to multiply the number of ways to arrange the remaining letters (Step 5) by the number of ways to arrange the Cs (Step 6).

Step 8: Perform the calculations

Let's calculate the number of different words using the above steps:

- Number of ways to arrange the remaining letters (Step 5):
- Remaining letters: S, O, V, H
- Number of ways to arrange these letters: 4!
- 4! = 4 x 3 x 2 x 1 = 24

- Number of ways to arrange the Cs (Step 6):
- Since there are two Cs, we have 2!
- 2! = 2 x 1 = 2

- Total number of different words (Step 7):
- Total = Number of ways to arrange the remaining letters x Number of ways to arrange the Cs
- Total = 24 x 2 = 48

Therefore, there are 48 different words that can be formed using all the letters of the word BUTTERSCOTVH, with the word BUTTER always squeezed between two Cs.