document.write( "Question 1174633: Eight cards each have a single digit written on them. The digits are 2, 2, 4, 5, 7, 7, 7, 7, respectively.
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Algebra.Com's Answer #800082 by Edwin McCravy(20056)\"\" \"About 
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a) Find the number of 8-digit numbers that can be formed.
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document.write( "The distinguishable arrangements of 2, 2, 4, 5, 7, 7, 7, 7 \r\n" );
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document.write( "If they were all distinguishable there would be 8!.\r\n" );
document.write( "But the 4 7's are indistinguishable, so we divide by 4!.\r\n" );
document.write( "Also the 2 2's are indistinguishable, so we divide by 2!.\r\n" );
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document.write( "So that's 8!/(4!2!) = 840 ways\r\n" );
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b) Find the number of 7-digit numbers that can be formed when all 7’s are included.
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document.write( "The digits are either\r\n" );
document.write( "Case 1: distinguishable arrangements of 2,2,4,7,7,7,7\r\n" );
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document.write( "[That's 7!/(4!2!) = 105]\r\n" );
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document.write( "or Case 2: distinguishable arrangements of 2,2,5,7,7,7,7\r\n" );
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document.write( "[That's also 7!/(4!2!) = 105]\r\n" );
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document.write( "or Case 3: distinguishable arrangements of 2,4,5,7,7,7,7\r\n" );
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document.write( "[That's 7!/4! = 210]\r\n" );
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document.write( "Total for all 3 cases: 105+105+210 = 420\r\n" );
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c) Find the number of 7-digit numbers that can be formed.
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document.write( "In addition to the 420 in part (b), the others are when the numbers are\r\n" );
document.write( "the distinguishable arrangements of 2,2,4,5,7,7,7.\r\n" );
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document.write( "That's 7!/(2!3!) = 420\r\n" );
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document.write( "Total = 420+420 = 840\r\n" );
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document.write( "Edwin

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