document.write( "Question 871432: Given the digits (1,1,2,2,2,5):\r
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document.write( "a) How many 6 digit numbers can be formed?
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document.write( "b) How many 6 digit numbers are divisible by 5? \n" );
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Algebra.Com's Answer #525586 by Edwin McCravy(20055)![]() ![]() You can put this solution on YOUR website! Given the digits (1,1,2,2,2,5): \n" ); document.write( "a) How many 6 digit numbers can be formed? \n" ); document.write( " \r\n" ); document.write( "We can place the two 1's in any 2 of the 6 positions. \r\n" ); document.write( "\r\n" ); document.write( "That's C(6,2) = 15 ways.\r\n" ); document.write( "\r\n" ); document.write( "For each of those 15 ways,\r\n" ); document.write( "\r\n" ); document.write( "we can place the three 2's in any 3 of the remaining 4 positions. \r\n" ); document.write( "That's C(4,3) = 4 ways.\r\n" ); document.write( "\r\n" ); document.write( "We then place the 5 in the only 1 remaining position. (1 way)\r\n" ); document.write( "\r\n" ); document.write( "Answer: 15×4×1 = 60 ways.\r\n" ); document.write( "\r\n" ); document.write( "------------------------ \n" ); document.write( "b) How many 6 digit numbers are divisible by 5? \n" ); document.write( " \r\n" ); document.write( "\r\n" ); document.write( "They must all end in 5.\r\n" ); document.write( "\r\n" ); document.write( "We place the 5 as the 6th digit. (1 way)\r\n" ); document.write( "\r\n" ); document.write( "We can place the two 1's in any 2 of the remaining 5 positions.\r\n" ); document.write( "That's C(5,2) = 10 ways.\r\n" ); document.write( "\r\n" ); document.write( "We then place the three 2's in the only 3 remaining positions. (1 way).\r\n" ); document.write( "\r\n" ); document.write( "Answer: 1×10×1 = 10 ways.\r\n" ); document.write( "\r\n" ); document.write( "Edwin\n" ); document.write( " |