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IV. Patterns: Using the letters - A B C D E in the box so that no letter comes twice in any timeV. Answer the following |
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Answer» The words of length 10 are formed using the letters A,B,C,D,E,F,G,H,I,J Let x be the number of words where no letter is repeated. CHOOSING he WORD where no letter is repeated can be done in 10! ways ∴x=10! Let y be the number of words where exactly one letter is repeated twice Since, one letter is repeated We can choose one repeatedly letter out of 10 letters and can be done in 10 C 1 ways, then place them on any two places, which can be done in 10 C 2 ways Now, choose 8 out of 9 REMAINING letters which can be done in 9 C 8 ways. And then, we can arrange that 8 non-repeated letters in 8! ways. ∴y= 10 C 1 × 10 C 2 × 9 C 8 ×8! =10×45×9×8! Then, 9x y = 9×10! 10×45×9×8! =5Step-by-step explanation: |
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