document.write( "Question 1118501: how many numbers can you form using the digits 2, 3, 4, 6, 5, 1, 0 if the numbers formed are even numbers with non-repeating digits? \n" ); document.write( "

Algebra.Com's Answer #733884 by ikleyn(52867) $\"\"$ $\"About$

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\n" ); document.write( "how many numbers can you form using the digits 2, 3, 4, 6, 5, 1, 0 if the numbers formed are even numbers with non-repeating digits?
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\n" ); document.write( "\n" ); document.write( "Let me edit your formulation in this way\r
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document.write( "    how many  numbers can you form using the digits 2, 3, 4, 6, 5, 1, 0 \r\n" );
document.write( "    if the numbers formed are even numbers with non-repeating digits?\r\n" );
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\n" ); document.write( "\n" ); document.write( "by adding the word/the words $\"highlight%287-digit%29\"$ . // I think it is exactly what you were going to ask.\r
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\n" ); document.write( "\n" ); document.write( "Solution\r
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\n" ); document.write( "\n" ); document.write( "Case 1: The last digit is 0 (zero)\r
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document.write( "Then the number of possibilities (of ways) is  6*5*4*3*2*1 = 720.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Case 2: the last digit is 2, or 4, or 6.\r
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document.write( "Then, since \"0\" can not be the leading digit, there are only 5 possibilities for the leading digit. \r\n" );
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document.write( "Moving from the second digit from the left to the sixth from the left, we have consequently 5, 4, 3, 2, 1 possibilities, that give, in all,\r\n" );
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document.write( "    (5*5*4*3*2*1)*3 =  1800 ways.\r\n" );
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document.write( "Finally, adding the numbers 720 and 1800, you get the total number of the possible numbers under the question 2520. \r\n" );
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\n" ); document.write( "\n" ); document.write( "Answer. 2520 numbers.\r
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\n" ); document.write( "\n" ); document.write( "Any other answer is incorrect, so ignore it.\r
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\n" ); document.write( "\n" ); document.write( "The lesson to learn from my solution:\r
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document.write( "    If you are asked to form a number/numbers from given digits, and if there is \"0\" (zero) among the given digits,\r\n" );
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document.write( "    then be very CAREFUL and REMEMBER that 0 is very special digit: it can not go first and can not be a leading digit.\r\n" );
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