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a)How many five-digit numbers can be formed using digits 3,0,6,6,6, and b) if the 3% of a number is 21,which is that number?

common
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  • 3% of 700 is 21, so I'm not sure how you're expecting to get a 5 digit number to have only 3% be 21. – JB King Jan 20 '16 at 20:56
  • I'm guessing a) and b) are unrelated questions. For a) there are 16: 30666, 36066, 36606, 36660, 60366, 60636, 60663, 63066, 63606, 63660, 66036, 66063, 66306, 66360, 66603, 66630. – cardboard_box Jan 20 '16 at 20:59
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    The two questions have nothing in common. Although the first question would be a lot of fun to answer[*] we are morally obligated to avoid doing your homework for you, which, these questions being so different, these obviously are. So to avoid downvotes and people calling you dirty names... please answer "What have you tried so far" and "what are your thoughts on it". That is the standard drill. Without showing any faith in effort, we will call you dirty names for expecting us to do your homework. [*] the second one is just tedious. – fleablood Jan 20 '16 at 21:02
  • ... or maybe we just will do your homework for you... – fleablood Jan 20 '16 at 21:04
  • @fleablood: Well, for some value of "we". – Brian Tung Jan 20 '16 at 21:13

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a) Every permutation of 5 digits are obtained by calculating 5!. Permutations with 0 as the first digit have to be ignored and there are 4! of those, so we are at 5! - 4!. The permutations of the 3 sixes are not different numbers, so we get (5! - 4!)/3!=16, which are the ones listed in the comment by cardboard_box.

b) $x*0.03=21 \Leftrightarrow x=700$

joedoe8585
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