MHB Is my solution for forming 10-letter words with restrictions correct?

  • Thread starter Thread starter evinda
  • Start date Start date
Click For Summary
The exercise involves calculating the number of 10-letter words that can be formed using the letters A, B, and C, with the restriction that the word cannot start or end with the same letter. The proposed solution is 3^10 - 2 * 3^9 + 3^8, which accounts for the total number of unrestricted words, subtracts cases where the first two letters are the same, and subtracts cases where the last two letters are the same, while adding back cases where both conditions overlap. The discussion confirms that the solution is correct. The final consensus validates the approach taken in the calculation.
evinda
Gold Member
MHB
Messages
3,741
Reaction score
0
Hello! (Wave)

I am given the following exercise:

How many words with $10$ lettrers can be formed with the letters $A,B,C$, when it is not allowed that the word begins or ends with two same letters.

I thought that the number of words is $$3^{10}-2 \cdot 3^9+3^8$$

because:

Number of words without restrictions: $3^{10}$

Number of words when the two first letters are the same: $3^{9}$

Number of words when the two last letters are the same: $3^{9}$

Number of words when the first two and the last two are the same: $3^{8}$Could you tell if it's right?Or am I wrong? :confused:
 
Physics news on Phys.org
I think your solution is correct.
 
Evgeny.Makarov said:
I think your solution is correct.

Nice! Thank you very much! (Clapping) (Clapping)
 

Thread 'How do E[X] and E[|X|] relate?'

Greetings, I am studying probability theory [non-measure theory] from a textbook. I stumbled to the topic stating that Cauchy Distribution has no moments. It was not proved, and I tried working it via direct calculation of the improper integral of E[X^n] for the case n=1. Anyhow, I wanted to generalize this without success. I stumbled upon this thread here: https://www.physicsforums.com/threads/how-to-prove-the-cauchy-distribution-has-no-moments.992416/ I really enjoyed the proof...
View full post »

Similar threads

High School Solve Combinations Puzzle: 5 Letters ABCDE
  • · Replies 18 ·
Replies
18
Views
3K
High School Where is the error in my reasoning about palindromes?
  • · Replies 3 ·
Replies
3
Views
2K
MHB Multi part Question involving probability and combinatrics with words
  • · Replies 3 ·
Replies
3
Views
3K
MHB The Telephone Numbering Plan in North America: Counting Possible Numbers
  • · Replies 4 ·
Replies
4
Views
7K
MHB How many words can be formed from the word SUCCESS without any repeated letters?
  • · Replies 2 ·
Replies
2
Views
2K
MHB Number of ways to arrange letters
  • · Replies 3 ·
Replies
3
Views
2K
MHB Solving Permutations Question with Restrictions
  • · Replies 3 ·
Replies
3
Views
1K
MHB Possible combinations for six digit license plates, numbers 0-9 and letters a-z.
  • · Replies 1 ·
Replies
1
Views
6K
Obtain the check digits in this problem
  • · Replies 1 ·
Replies
1
Views
1K
Number of different license plates
  • · Replies 2 ·
Replies
2
Views
2K