document.write( "Question 964710: How many positive integers are there less than 900 such that all digits are odd? \n" ); document.write( "

Algebra.Com's Answer #589539 by macston(5194) $\"\"$ $\"About$

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There are three cases to consider:
\n" ); document.write( "1)One digit numbers
\n" ); document.write( "2)Two digit numbers
\n" ); document.write( "3)three digit numbers
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\n" ); document.write( "For one digit numbers, 5 are odd:1,3,5,7,9 so we add these to our total:5
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\n" ); document.write( "For two digit numbers, we have five choices for the tens digit and five choices for the units digit so we add 5 x 5=25 more to our total:5+25=30
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\n" ); document.write( "For three digit numbers, we only have 4 choices for the hundreds digit (numbers starting with 9 are greater than 900) and still five choices for tens and five for units so we add 4 x 5 x 5=100 to our total:30+100=130
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\n" ); document.write( "ANSWER There are 130 numbers less than 900 with only odd digits.\r
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