In the Vigornii alphabet there are consonants and vowels. How many different arrangements of letters can be made if exactly vowels must be used and no repetition of letters is allowed?

Source: NCTM Mathematics Teacher, February 2006

**SOLUTION**

1. Choose places out of places to put the vowels

2. Put vowels out of vowels in the chosen places

3. In the remaining places put consonants out of consonants

There are different arrangements.

**Answer**: 40320

*Alternative solution
*1. Choose vowels out of vowels

2. Choose consonants out of consonants

3. How many ways can we form a word with vowels and consonants?

4. For each of the five-letter words how many different ways can we arrange the letters?

Advertisements