document.write( "Question 1167300: a) How many seven-digit telephone numbers have one digit which is a multiple of 4 and six digits which are
\n" ); document.write( "not a multiple of 4?
\n" ); document.write( "b) How many seven-digit telephone numbers have three digits which are a multiple of 4 and four digits which
\n" ); document.write( "are not a multiple of 4?
\n" ); document.write( "c) Continuing the pattern, and adding the disjoint possibilities, answer the broader question: How many
\n" ); document.write( "seven-digit telephone numbers have exactly an odd number of digits which are a multiple of 4?
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Algebra.Com's Answer #852099 by ikleyn(52778) $\"\"$ $\"About$

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\n" ); document.write( "a) How many seven-digit telephone numbers have one digit which is a multiple of 4 and six digits which are
\n" ); document.write( "not a multiple of 4?
\n" ); document.write( "b) How many seven-digit telephone numbers have three digits which are a multiple of 4 and four digits which
\n" ); document.write( "are not a multiple of 4?
\n" ); document.write( "c) Continuing the pattern, and adding the disjoint possibilities, answer the broader question: How many
\n" ); document.write( "seven-digit telephone numbers have exactly an odd number of digits which are a multiple of 4?
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document.write( "(a)  There are 7 possible positions for one digit which is multiple of 4.\r\n" );
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document.write( "     It gives us the factor (multiplier) 7.\r\n" );
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document.write( "     There are 3 possibilities for a digit multiple of 4:  '0', '4', '8'.\r\n" );
document.write( "     It gives us the factor (multiplier) 3.\r\n" );
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document.write( "     In the rest 6 positions, we may have any of 10-3 = 7 digits 1, 2, 3, 5, 6, 7, 9 independently.\r\n" );
document.write( "     It gives us the factor (multiplier)  .\r\n" );
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document.write( "     Thus the  ANSWER  to question (a) is the product of factors   =  = 2,470,629.\r\n" );
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document.write( "     Part (a) is complete.\r\n" );
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document.write( "(b)  Three digits which are multiple of 4, can be placed in   =  = 7*5 = 35 different ways.\r\n" );
document.write( "     These three digits can be 0, 4, 8 independently.\r\n" );
document.write( "     So far, we have the multiplier   = 35*9.\r\n" );
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document.write( "     The remaining 4 digits are in the remaining positions.\r\n" );
document.write( "     These remaining digits can be any of 10-3 = 7 digits 1, 2, 3, 5, 6, 7, 9.\r\n" );
document.write( "     It gives us the multiplier  .\r\n" );
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document.write( "     Thus the  ANSWER  to question (b) is the product of factors  = 35*(3^3)*(7^4) = 2268945.\r\n" );
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document.write( "     Part (b) is complete.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Thus parts (a) and (b) are just solved.\r
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\n" ); document.write( "\n" ); document.write( "With it, you got from me the idea how to solve for one special digit and for 3 special digits.\r
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\n" ); document.write( "\n" ); document.write( "The move forward for 5 special digits and for 7 special digits is very similar to it.
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\n" ); document.write( "\n" ); document.write( "I will stop at this point and will not solve (c) in order for do not turn my post into mess.\r
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\n" ); document.write( "\n" ); document.write( "Continue in the same manner to complete for part (c).\r
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