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find the number of distinguishable five-letter permutation that can be formed from the letter in the word 'WINDOW'?
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document.write( "There are two cases.\r\n" );
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document.write( "Case 1: Those 5-letter permutations that contain only one W.\r\n" );
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document.write( "They are the permutations of WINDO of which there are 5! or 120.\r\n" );
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document.write( "Case 2. Those 5-letter permutations that contain both W's.\r\n" );
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document.write( "Choose the positions {1st,2nd,3rd,4th,5th} for the 2 W's in 5C2 = 10 ways\r\n" );
document.write( "Choose the letter for the leftmost unchosen position 4 ways, {I,N,D, or O}\r\n" );
document.write( "Choose the letter for the leftmost still unchosen position 3 ways.\r\n" );
document.write( "Choose the letter for the 1 remaining unchosen position 2 ways.\r\n" );
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document.write( "That's 10*4*3*2 = 240 ways\r\n" );
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document.write( "Grand total = 120+240 = 360\r\n" );
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document.write( "That's the answer.\r\n" );
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document.write( "FYI, Here is an alternate way to do Case 2, where we choose the letters\r\n" );
document.write( "instead of the positions.\r\n" );
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document.write( "Case 2. Those that contain both W's.\r\n" );
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document.write( "We choose the two W's 1 way. \r\n" );
document.write( "We choose the other 3 letters from {!,N,D,O}. That's 4 choose 3 \r\n" );
document.write( "or 4C3 = 4 ways.\r\n" );
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document.write( "Each has 2 indistinguishable W's so the number of permutations\r\n" );
document.write( "is 5!/2! = 120/2 = 60.\r\n" );
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document.write( "That's (1)(4)(60) = 240 ways for Case 2\r\n" );
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document.write( "Edwin \n" );
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