document.write( "Question 1205223: Freddie has forgotten the 6-digit code that he uses to lock his briefcase. He knows that he did not
\n" ); document.write( "repeat any digit and that he did not start his code with a zero.
\n" ); document.write( "(i) Find the number of different 6-digit numbers he could have chosen. \r
\n" ); document.write( "\n" ); document.write( "Freddie also remembers that his 6-digit code is divisible by 5.
\n" ); document.write( "(ii) Find the number of different 6-digit numbers he could have chosen. \n" ); document.write( "

Algebra.Com's Answer #841882 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "Freddie has forgotten the 6-digit code that he uses to lock his briefcase. He knows that he did not
\n" ); document.write( "repeat any digit and that he did not start his code with a zero.
\n" ); document.write( "(i) Find the number of different 6-digit numbers he could have chosen. \r
\n" ); document.write( "\n" ); document.write( "Freddie also remembers that his 6-digit code is divisible by 5.
\n" ); document.write( "(ii) Find the number of different 6-digit numbers he could have chosen.
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document.write( "       The solution and the answer to question (i)\r\n" );
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document.write( "The number of different 6-digit codes he could have chosen is\r\n" );
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document.write( "     9*9*8*7*6*5 = 136080.\r\n" );
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document.write( "Any of 9 = 10-1 digits can be in 1st position (any except of 0).\r\n" );
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document.write( "Any of 9 remaining digits can be in 2nd position (0 is allowed now in the 2nd position).\r\n" );
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document.write( "Any of 8 remaining digits can be in 3rd position.\r\n" );
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document.write( "And so on, till the end.\r\n" );
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document.write( "       The solution and the answer to question (ii)\r\n" );
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document.write( "The number of different 6-digit codes he could have chosen is\r\n" );
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document.write( "     9*8*7*6*5*1 + 8*8*7*6*5*1 = 15120 + 13440 = 28560.\r\n" );
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document.write( "First addend is for codes that end with 0 - for them, there is only 1 choice for the 6th digit.\r\n" );
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document.write( "Second addend is for codes that end with 5 - so, there is only 1 choice for the 6th digit.\r\n" );
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