Counting problem (aabbcccdddd)

In summary, there are 62 possible arrangements of the word "aabbcccdddd" if only 3 letters are used. This can be calculated by counting the number of ways to permute using 1 letter of each, adding the number of ways to permute using 1 of one letter and 2 of another, and adding 2 for the arrangements ccc and ddd. The final answer is 62.
  • #1
ashi_mashi
8
0
hi everyone...
how many arrangements of this word "aabbcccdddd" is possible if we only use 3 of them? I know if we could use all of them it would just be 11!/(2!2!3!4!), but what if we only use 3? :confused:

Thanks in advance
 
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  • #2
I assume you mean 3 letters in the arrangement. First count the number of ways to permute using 1 letter of each, then in addition to that count the number of ways to permute using 1 of one letter and 2 of another, and then add 2 for the arrangements ccc and ddd.
 
  • #3
ok..thanks...so the answer would be 52?
 
  • #4
Not quite what I got--maybe you added wrong at the end?
 
  • #5
umm...i tried it again...i got 62 (checked it 3 times!)
 
  • #6
Yep, 62 is what I got. You said 52 the other time.
 
  • #7
thanks a lot
 

Related to Counting problem (aabbcccdddd)

1. What is the counting problem (aabbcccdddd)?

The counting problem (aabbcccdddd) is a mathematical problem that involves determining the number of unique arrangements of letters in a string, where each letter appears a specific number of times. In this case, the string consists of two "a"s, two "b"s, three "c"s, and four "d"s.

2. How do you approach solving the counting problem (aabbcccdddd)?

To solve the counting problem (aabbcccdddd), you can use the concept of permutations and combinations. First, determine the total number of letters in the string (11 in this case). Then, calculate the number of ways to arrange the letters, taking into account the repeated letters. In this case, it would be 11! / (2! x 2! x 3! x 4!) = 34650.

3. Can the counting problem (aabbcccdddd) be solved using a formula?

Yes, the counting problem (aabbcccdddd) can be solved using the formula n! / (n1! x n2! x n3! ...), where n is the total number of letters and n1, n2, n3, etc. are the number of times each letter is repeated. In this case, it would be 11! / (2! x 2! x 3! x 4!).

4. Is there a way to solve the counting problem (aabbcccdddd) without using a formula?

Yes, you can also solve the counting problem (aabbcccdddd) by manually listing out all the possible arrangements of letters. However, this method may be more time-consuming and prone to errors, especially for longer strings with more repeated letters.

5. How can the counting problem (aabbcccdddd) be applied in real-life situations?

The counting problem (aabbcccdddd) has various applications in different fields, such as computer science, genetics, and linguistics. For example, it can be used to calculate the number of possible DNA sequences, the number of unique words in a language, or the number of distinct combinations in a password.

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