Question

If you have 11 letters, assuming any combination of the letters makes a word, and letters can be used more than once, how many 1 letter words? 3 letter words? 4 letter words? 6 letter words? 11 letter words?

Answer 1

Conditions

If you have 11 letters, assuming any combination of the letters makes a word, and letters can be used more than once, how many 1 letter words? 3 letter words? 4 letter words? 6 letter words? 11 letter words?

Solution

1) There are 11 letters and one-lettered words. The one-lettered words can be constructed in 11 different ways.

2) There are 11 letters and three-lettered words. They can be constructed by taking $1^{\text{st}}$ letter in 11 ways, then taking $2^{\text{nd}}$ letter in 10 ways and $3^{\text{rd}}$ – in 9 ways. So there are $11*10*9=990$ words.

3) 4 letter words – $11*10*9*8=7920$

4) 11 letter words – $11*10*9*8*7*6*5*4*3*2*1=11!=39916800$ words