document.write( "Question 1127738: if a permutation of the word \"white\" is selected at random, find the probability that the permutation
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document.write( "A) begins with a consonant
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document.write( "B) ends with a vowel
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document.write( "C) has the consonants and vowels alternating\r
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document.write( "please give a explanatiion \n" );
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Algebra.Com's Answer #744421 by Edwin McCravy(20062) You can put this solution on YOUR website! if a permutation of the word \"white\" is selected at random, \n" ); document.write( "find the probability that the permutation \n" ); document.write( " \r\n" ); document.write( "The denominator of each of the probabilities will be 5P5 = 5! = 120\r\n" ); document.write( " \n" ); document.write( "A) begins with a consonant \n" ); document.write( " \r\n" ); document.write( "Pick the 1st letter any of 3 ways (w, h or t)\r\n" ); document.write( "Arrange the remaining 4 letters in 4P4 = 4! = 24 ways\r\n" ); document.write( "\r\n" ); document.write( "That's 3∙24 = 72 ways\r\n" ); document.write( "\r\n" ); document.write( "Probability = 72/120 = 3/5\r\n" ); document.write( " \n" ); document.write( "B) ends with a vowel \n" ); document.write( " \r\n" ); document.write( "Pick the 5th letter either of 2 ways (i or e)\r\n" ); document.write( "Arrange the remaining 4 letters in 4P4 = 4! = 24 ways\r\n" ); document.write( "\r\n" ); document.write( "That's 2∙24 = 48 ways\r\n" ); document.write( "\r\n" ); document.write( "Probability = 48/120 = 2/5\r\n" ); document.write( " \n" ); document.write( "C) has the consonants and vowels alternating \n" ); document.write( " \r\n" ); document.write( "CVCVC\r\n" ); document.write( "\r\n" ); document.write( "The 3 consonants can be rearranged in the 1st, 3rd, and 5th\r\n" ); document.write( "positions in 3P3 = 3! = 6 ways.\r\n" ); document.write( "The 2 vowels can be rearranged in the 2nd and 4th\r\n" ); document.write( "positions in 2P2 = 2! = 2 ways.\r\n" ); document.write( "\r\n" ); document.write( "That's 6∙2 = 12 ways\r\n" ); document.write( "\r\n" ); document.write( "Probability = 12/120 = 1/10\r\n" ); document.write( "\r\n" ); document.write( "Edwin\r \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |