document.write( "Question 1193916: How many different four-digit numbers are possible if each digit of the number is either 0,1,2,3,4 or 5, and numbers starting with 3 cannot be even?\r
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document.write( "The textbook answer is 972.\r
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document.write( "Can someone tell me how to solve this problem? \n" );
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Algebra.Com's Answer #825971 by Edwin McCravy(20055)![]() ![]() You can put this solution on YOUR website! \r\n" ); document.write( "\r\n" ); document.write( "First let's calculate how many 4-digit numbers have digits from\r\n" ); document.write( "{0,1,2,3,4,5}, \r\n" ); document.write( "regardless of whether they start with 3 or are odd or even. Then \r\n" ); document.write( "we'll calculate how many start with 3 and are even, and subtract. \r\n" ); document.write( "\r\n" ); document.write( "A. Since a 4-digit number can't start with 0, the ways to \r\n" ); document.write( "choose the 1st digit are any one of these: {1,2,3,4,5}. \r\n" ); document.write( "How many choices is that? _____\r\n" ); document.write( "\r\n" ); document.write( "B. The ways to choose the 2nd digit are any of these:\r\n" ); document.write( "{0,1,2,3,4,5}. How many choices is that? _____\r\n" ); document.write( "\r\n" ); document.write( "C. The ways to choose the 3rd digit are any of these:\r\n" ); document.write( "{0,1,2,3,4,5}. How many choices is that? _____\r\n" ); document.write( "\r\n" ); document.write( "D. The ways to choose the 4th digit are any of these:\r\n" ); document.write( "{0,1,2,3,4,5}. How many choices is that? _____\r\n" ); document.write( "\r\n" ); document.write( "E. Multiply the answers to questions A,B,C, and D together.\r\n" ); document.write( "What do you get? _____\r\n" ); document.write( "\r\n" ); document.write( "Now let's calculate how many we need to subtract from the answer\r\n" ); document.write( "to question E.\r\n" ); document.write( "\r\n" ); document.write( "We must not include any 4-digit numbers that start with 3 that\r\n" ); document.write( "are even. So let's see how many there are of those>\r\n" ); document.write( "\r\n" ); document.write( "F. There is only one choice for the first digit of the numbers\r\n" ); document.write( "we want to NOT include. How many choices is that? 1 \r\n" ); document.write( "(I filled that in for you as 1 for it's the 1 digit \"3\"). \r\n" ); document.write( "\r\n" ); document.write( "G. The ways to choose the 2nd digit are any of these:\r\n" ); document.write( "{0,1,2,3,4,5}. How many choices is that? _____\r\n" ); document.write( "\r\n" ); document.write( "H. The ways to choose the 3rd digit are any of these:\r\n" ); document.write( "{0,1,2,3,4,5}. How many choices is that? _____\r\n" ); document.write( "\r\n" ); document.write( "I. But since the numbers we don't want to count are even, the\r\n" ); document.write( "last (fourth) digit must be one of these (0, 2, 4). How many\r\n" ); document.write( "choices is that? _____\r\n" ); document.write( "\r\n" ); document.write( "J. Multiply the answers for questions F,G,H, and I. What do\r\n" ); document.write( "you get? _____\r\n" ); document.write( "\r\n" ); document.write( "K. Subtract the answer to J from the answer to E. What do you\r\n" ); document.write( "get? _____\r\n" ); document.write( "\r\n" ); document.write( "Should be 972. If you don't get 972, tell me your answers to the\r\n" ); document.write( "above questions in the thank-you note form below and I'll get back to\r\n" ); document.write( "you by email.\r\n" ); document.write( "\r\n" ); document.write( "Edwin\n" ); document.write( " |