document.write( "Question 890984: Consider strings of length 6 which contain letters only from the set { P,Q,R,S,T} and digits from { 1,3,5,7,9}. for example TPR5Q7 is such a string.Suppose repetition allowed.
\n" ); document.write( "A) How many different strings are there?
\n" ); document.write( "B) How may of these strings have no P?
\n" ); document.write( "C) How may of these strings have at least one P?
\n" ); document.write( "D) How may of these strings have exactly two P's and one 7? \n" ); document.write( "
Algebra.Com's Answer #539451 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
Consider strings of length 6 which contain letters only from the set { P,Q,R,S,T} and digits from { 1,3,5,7,9}. for example TPR5Q7 is such a string.Suppose repetition allowed.
\n" ); document.write( "A) How many different strings are there?
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document.write( "10 ways to choose the 1st character.\r\n" );
document.write( "10 ways to choose the 2nd character.\r\n" );
document.write( "10 ways to choose the 3rd character.\r\n" );
document.write( "10 ways to choose the 4th character.\r\n" );
document.write( "10 ways to choose the 5th character.\r\n" );
document.write( "10 ways to choose the 6th character.\r\n" );
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document.write( "106 = 1000000\r\n" );
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\n" ); document.write( "B) How many of these strings have no P?
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document.write( "9 ways to choose the 1st character.\r\n" );
document.write( "9 ways to choose the 2nd character.\r\n" );
document.write( "9 ways to choose the 3rd character.\r\n" );
document.write( "9 ways to choose the 4th character.\r\n" );
document.write( "9 ways to choose the 5th character.\r\n" );
document.write( "9 ways to choose the 6th character.\r\n" );
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document.write( "96 = 531441.\r\n" );
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\n" ); document.write( "C) How many of these strings have at least one P?
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document.write( "We subtract the result of B) from the result of A):\r\n" );
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document.write( "1000000 - 531441 = 468559\r\n" );
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\n" ); document.write( "D) How may of these strings have exactly two P's and one 7?
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document.write( "Choose the positions for the two P's in C(6,2) = 15 ways.\r\n" );
document.write( "Choose the position for the one 7 as any of the remaining 4 ways.\r\n" );
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document.write( "That leaves 3 remaining positions to fill from the set of 8 \r\n" );
document.write( "characters {Q,R,S,T,1,3,5,9}.\r\n" );
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document.write( "Fill the first remaining position any of these 8 ways.\r\n" );
document.write( "Fill the second remaining position any of these 8 ways.\r\n" );
document.write( "Fill the third remaining position any of these 8 ways.\r\n" );
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document.write( "Answer: 15󫶜󭅌 = 30720 ways.\r\n" );
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document.write( "Edwin
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