document.write( "Question 1207741: If each coded item in a catalog begins with 3 distinct letters followed by 4 distinct nonzero digits, find the probability of randomly selecting one of these coded items with the first letter a vowel and the last digit even.
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Algebra.Com's Answer #845777 by ikleyn(52788) $\"\"$ $\"About$

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\n" ); document.write( "If each coded item in a catalog begins with 3 distinct letters followed by 4 distinct nonzero digits,
\n" ); document.write( "find the probability of randomly selecting one of these coded items with the first letter a vowel
\n" ); document.write( "and the last digit even.
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\n" ); document.write( "\n" ); document.write( " The problem does not say that in the catalog all possible positions are filled,\r
\n" ); document.write( "\n" ); document.write( " but I will assume it as a context (by default).\r
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document.write( "The number of all possible positions is  TOTAL = 26*25*24*9*8*7*6,\r\n" );
document.write( "so this is the number of all possible items in the catalog.\r\n" );
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document.write( "The structure of this formula is clear and does not require more explanations.\r\n" );
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document.write( "To get the number of items with special codes, in the formula above we need \r\n" );
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document.write( "        - to replace the total number of letters 26 by the number of vowels 5,\r\n" );
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document.write( "    and\r\n" );
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document.write( "         - to replace the total number of non-zero digits 9 by the number of nonzero even digits 4.\r\n" );
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document.write( "So, the formula for the number of favorable items becomes  FAVORABLE = 5*25*24*4*8*7*6.\r\n" );
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document.write( "The probability under the question is\r\n" );
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document.write( "    P =  = .\r\n" );
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document.write( "After reducing common factors in the fraction, we get\r\n" );
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document.write( "    P =  =  = 0.08547  (rounded).    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "For tutor @greenestamps:\r
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\n" ); document.write( "\n" ); document.write( "        In your response, you should use \" 4 \" for the number of last non-zero even digits.\r
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\n" ); document.write( "\n" ); document.write( "To a reader:\r
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\n" ); document.write( "\n" ); document.write( "        In his post, @greenestamps writes that there are no restrictions on other letters or digits.\r
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\n" ); document.write( "\n" ); document.write( "        It depends on point of view. The problem says that the letters are distinct and the digits are distinct. \r
\n" ); document.write( "\n" ); document.write( "        So, I consider it as restrictions.\r
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\n" ); document.write( "\n" ); document.write( "        It is why I wrote my long solution to show explicitly, how to solve the problem accounting for these restrictions. \r
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