2

How many numbers with $3$ digits can be formed with the digits $1,2,3,4,5$

  • if there is no restriction at the repetition of the digits

  • how many if no digit can be repeated more than twice

  • and how many if repetitions are not allowed

For the first subquestion, I thought that $5^3$ numbers with $3$ digits can be formed.

For the third subquestion, I thought that $5 \cdot 4 \cdot 3$ can be formed with $3$ digits.But which is the general formula?

How can I find how many numbers with $3$ digits can be formed,for the second subquestion?

Matthew Conroy
  • 11,234
evinda
  • 7,823
  • Suppose you are picking each digit out of a bag, but returning it into the bag only once. How many digits can you pick out of the bag each time out of the 3 times? –  Jun 02 '14 at 10:26
  • For second part: (1) from total number of numbers, remove those that have three repeats or (2) add number of numbers without repeat digits to number of number of numbers with exactly one digit occurring twice – tpb261 Jun 02 '14 at 10:27
  • What do you mean by "But which is the general formula?" ? – tpb261 Jun 02 '14 at 10:28
  • @tpb261 The formula that we use at the third subquestion to find $5 \cdot 4 \cdot 3$... – evinda Jun 02 '14 at 10:29
  • @tpb261 Which formula do I have to use for the second subquestion? – evinda Jun 02 '14 at 10:31
  • @wiz3kid Which formula do I have to use for the second subquestion? Could you give me a hint???? – evinda Jun 02 '14 at 10:32
  • I'd suggest not to worry as much about the formula, as about the procedure/logic. For computing $5.4.3$, it is number of permutations of $r$ objects from $n$ – tpb261 Jun 02 '14 at 10:36
  • You can use Principle of inclusion and exclusion – Karo Jun 02 '14 at 20:29

1 Answers1

3

@evinda

Which formula do I have to use for the second subquestion?

$$5^3 - 5 = 120$$

bobbym
  • 2,546