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How many 10-letter “words” one can write using 4 letters H and 6 letters T?

User Denae
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1 Answer

4 votes

Answer:

210

Explanation:

There are 210 total possible "words" that can be written using 4 letters H and 6 letters T.

To find the total number of possible words, we can use the combination formula:

C(n,r) = n! / (r! * (n-r)!)

Where n is the total number of letters (in this case, 10) and r is the number of a specific letter (either H or T).

We can find the total number of possible words by finding the number of words with 4 H's and 6 T's, and adding it to the number of words with 6 H's and 4 T's.

For the first case (4 H's and 6 T's), the number of possible words is:

C(10,4) = 10! / (4! * 6!) = 210

For the second case (6 H's and 4 T's), the number of possible words is:

C(10,6) = 10! / (6! * 4!) = 210

Adding these two values gives us a total of 210 + 210 = 420 possible words. However, since each of these words is considered a distinct possibility, we must divide the total by 2 to account for the duplication. This gives us a final total of 420 / 2 = 210 possible 10-letter "words" using 4 letters H and 6 letters T.

I hope this helps! Let me know if you have any other questions or need further assistance.

User Brendan Hannemann
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