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Worked Examples · Example 15

Q.How many three digit numbers can be formed using the digits 0, 1, 3, 5 and 8.

(i) If repetition of digits is not allowed
(ii) If repetition of digits is allowed.
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Fill the hundreds, tens and units places by the multiplication principle, remembering the hundreds digit cannot be 00.

[!FORMULA]

Fundamental principle of counting: if a task is done in stages with m1,m2,m3m_1, m_2, m_3 choices respectively, the total number of ways =m1×m2×m3= m_1 \times m_2 \times m_3. The leftmost (hundreds) digit of a number can never be 00.

  1. Available digits: {0,1,3,5,8}\{0,1,3,5,8\}, so n=5n=5 digits in all.
  2. (i) Repetition not allowed:
    • Hundreds place: cannot be 00 ⇒\Rightarrow 44 choices (1,3,5,81,3,5,8).
    • Tens place: any digit except the one already used ⇒\Rightarrow 44 choices (now 00 is allowed).
    • Units place: any digit except the two already used ⇒\Rightarrow 33 choices.
    • Total =4×4×3=48= 4 \times 4 \times 3 = 48.
  3. (ii) Repetition allowed: …
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