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

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Solution

Calculating the number of words that can be formed from letters $H, T, G, B, X, X, T, L, N, J$ .
We have been given $10$ letters among which there are two $X$ .
Therefore, the number of letters will be
$= \frac{10!}{2} = \frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{2} = 1814400$
Hence, $1814400$ words can be formed with the given letters.

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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.

Calculating the number of words that can be formed from letters H,T,G,B,X,X,T,L,N,J.We have been given 10 letters among which there are two X.Therefore, the number of letters will be=10!2=10×9×8×7×6×5×4×3×2×12=1814400Hence, 1814400 words can be formed with the given letters.

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