**How plenty of different 10 letter words (real or imaginary) can be developed from the complying with letters**

### Answer

**1.H,T,G,B,X,X,T,L,N,J**

Consider the following letters:

\mathrmH, \mathrmT, \mathrmG, \mathrmB, \mathrmX, \mathrmX, \mathrmT, \mathrmL, \mathrmN, \mathrmJ

Find different 10 letter words have the right to be developed from the above letters.

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Number of letter in the word =10

The number of repititions that the letter in the respective word =2 ! 2 !

Recall the formula,

The total number of words in a given letters =\fracn !a ! b ! right here n= variety of letters in the word

a ! b != The number of repititions the the letters in the respective word

Given letters are H, T, G, B, X, X, T, L, N, J .

Number of letters in words "n"^\prime=10

a=2 ! (Letter T repeating 2 times) b=2 ! (Letter X repeating 2 time ) Therefore, total number of words =\frac10 !2 ! 2 !.

See more: American College Of Rheumatology 2017, 2017 Acr/Arhp Annual Meeting Archives

\beginaligned=\frac10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1(2 \cdot 1)(2 \cdot 1) \\=907200\endaligned**Thus, the total number of words is 907200**

**2.X,D,M,B,U,A D,F,U,Q**

**3.E,S,Z,B,X,D,S,U,I,V**

number of ways to kinds 2 S and rest 6 different letters =10!/(2!*1!*1!*1!*1!*1!*1!*1!*1!)

=3628800/2

=1814400

**4.Y,A,Z,Q,P,I,A,D,R,H**

The number of 10 -letter words ( actual or imaginary) have the right to be developed from the Y,A,Z,Q,P,I,A,D,R,H letters is 10! = 10*9*8*7*6*5*4*3*2*1 = 3628800

Answer: 3628800

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