document.write( "Question 1195969: 2. If the permutation of the word WHITE is selected at random, how many of the permutations
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Algebra.Com's Answer #828613 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "If the permutation of the word WHITE is selected at random, how many of the permutations
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\n" ); document.write( "iii. Has a consonant and vowels alternating?
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document.write( "(i)   The total number of permutations of the letters W,H,I,T,E is 5! = 5*4*3*2*1 = 120.\r\n" );
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document.write( "      Of them, the number of permutations starting with the consonant W is 4! = 4*3*2*1 = 24;\r\n" );
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document.write( "               the number of permutations starting with the consonant H is another 4! = 4*3*2*1 = 24;\r\n" );
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document.write( "               the number of permutations starting with the consonant T is another 4! = 4*3*2*1 = 24.\r\n" );
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document.write( "       The total number of permutations starting with the consonant is 3*24 = 72.    ANSWER\r\n" );
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document.write( "(ii)   Similar reasoning with the last letters gives the number of permutations for question (ii)  2*24 = 48.    ANSWER\r\n" );
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document.write( "(iii)  For alternating locations, we have these permutations  CVCVC, where C is a place holder  \r\n" );
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document.write( "       for any of the three consonants and V is a place holder for any of the two participating vowels.\r\n" );
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document.write( "       So, the number of the alternate permutations is 3!*2! = 6*2 = 12.       ANSWER\r\n" );
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