Lots of Words

Probability Level 2

How many "words" with five letters or less can be formed using letters from the word 'WORDS' such that

  • Letters may be repeated.
  • Words must have at least one letter.


The answer is 3905.

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Oliver Papillo by Oliver Papillo , 18, Australia

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1 solution

Oliver Papillo
Dec 31, 2016

Using the rule of product , the number of n n -letter words is equal to 5 n 5^n , as there are 5 5 ways of choosing each letter, and n n letters.

This means the total number of "words" is equal to 5 5 + 5 4 + 5 3 + 5 2 + 5 1 = 3905 5^5 + 5^4 + 5^3 + 5^2 + 5^1 = 3905

2 Helpful 1 Interesting 0 Brilliant 0 Confused

The problem here is that a word is not just a jumble of letters.

Allen Helmer - 1 year, 10 months ago

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