Combinatorics problem - Permutations of ABDEFGH

In summary, there are 120 permutations of the letters ABCDEFGH that contain the strings BA and FGH, following the example in the book where all clusters are in alphabetical order. The order of the clusters being alphabetical does not affect the number of permutations.
  • #1
Goldenwind
146
0
In theory I'm done this question, but would like to get it checked.

22) How many permutations of the letters ABCDEFGH contain
c) the strings BA and FGH?

Answer:

5 objects: BA, C, D, E, FGH.
Total: 5! = 120

This is following the example in the book. However, the example only has one cluster (Where a cluster is like BA, or FGH), and all of the book's clusters are in alphabetical order.

For something like this, where we have two clusters, and it's BA, not AB, does my method still work?
 
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  • #2
That the order is alphabetical makes absolutely no difference. You knew that in your heart, right?
 
  • #3
That's what I figured, hence how I got my answer, but just wanted to check to be sure.
 

FAQ: Combinatorics problem - Permutations of ABDEFGH

1. What is combinatorics and how does it apply to this problem?

Combinatorics is a branch of mathematics that deals with counting and arranging objects in a systematic way. In this problem, we are looking at all possible arrangements of the letters A, B, D, E, F, G, and H.

2. How many permutations are possible for the given letters?

There are 7 letters in total, so there are 7 factorial (7!) possible permutations. This means there are 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040 possible permutations.

3. How do you calculate the number of permutations when some letters are repeated?

In this problem, the letters E and G are repeated. When calculating the number of permutations, we divide the total number of permutations by the factorial of the number of repeated letters. So in this case, we divide 7! by 2! for the two E's and 2! for the two G's, resulting in 7! / (2! x 2!) = 1260 possible permutations.

4. Is there a specific order in which the letters must be arranged?

Yes, the order of the letters matters in this problem. A different arrangement of the same letters will result in a different permutation. For example, ABD is a different permutation than BDA.

5. Are there any restrictions or conditions for the permutations in this problem?

No, there are no specific restrictions or conditions for the permutations in this problem. We are simply looking at all possible arrangements of the given letters.

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