ofraun4ys5

2023-03-31

How many different 10 letter words (real or imaginary) can be formed from the following letters
H,T,G,B,X,X,T,L,N,J.

rangiranitlh9

To find the number of different 10-letter words that can be formed from the given letters (H, T, G, B, X, X, T, L, N, J), we can use the concept of permutations.
In this case, we have a total of 10 letters, but some of them are repeated. Specifically, the letter 'X' appears twice.
The number of different permutations of these letters can be calculated using the formula for permutations with repetition:
$\frac{n!}{{n}_{1}!·{n}_{2}!·\dots ·{n}_{k}!}$
where $n$ is the total number of letters and ${n}_{1},{n}_{2},\dots ,{n}_{k}$ are the frequencies of each repeated letter.
In this case, we have:
- $n=10$ (total number of letters)
- ${n}_{1}=2$ (frequency of 'X')
- ${n}_{2}=1$ (frequency of each of the remaining letters: H, T, G, B, L, N, J)
Using the formula, we can calculate the number of different permutations:
$\frac{10!}{2!·1!·1!·1!·1!·1!·1!·1!·1!}$
Simplifying the expression, we have:
$\frac{10!}{2!}=\frac{10×9×8×7×6×5×4×3×2×1}{2×1}=907,200$
Therefore, the number of different 10-letter words that can be formed from the given letters is $\overline{)907,200}$.

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