SOLUTION: Call an integer dangerous if no two of its digits are equal and no digit is 2. Call an integer sexy if all its digits are odd. How many four-digit integers are either sexy or dange

Algebra ->  Permutations -> SOLUTION: Call an integer dangerous if no two of its digits are equal and no digit is 2. Call an integer sexy if all its digits are odd. How many four-digit integers are either sexy or dange      Log On


   



Question 1065991: Call an integer dangerous if no two of its digits are equal and no digit is 2. Call an integer sexy if all its digits are odd. How many four-digit integers are either sexy or dangerous?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The 1st digit must exclude 0 or 2, so
there are 8 choices for the 1st digit
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The 2nd 2nd digit excludes the 1st digit
and 2, so there are 8 choices
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The 3rd digit excludes 1st and 2nd digits
and 2, so there are 7 choices
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There are 6 choices for the 4th digit
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There are +8%2A8%2A7%2A6+=+2688+- dangerous numbers
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So there are no overlaps with sexy integers
count the number of dangerous integers
that have all odd digits
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5 choices for the 1st ( dangerous integer ) digit
are odd
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4 choices for the 2nd digit are odd
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3 choices the the 3rd are odd
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2 choices for the 4th are odd
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There are +5%2A4%2A3%2A2+=+120+ dangerous numbers that are sexy
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+2688+-+120+=+2568+
There are 2568 dangerous numbers that are NOT sexy
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There are +5%2A5%2A5%2A5+=+625+ sexy numbers
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There are +2568+%2B+625+=+3193+ 4 digit numbers
that are EITHER sexy or dangerous
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Definitely get a 2nd opinion on this!!!
I could easily be missing something