# The letters of the word CONSTANTINOPLE are written on 14 cards, one of each card. The cards are shuffled and then arranged in a straight line. How many arrangements are there where no two vowels are next to each other?

##### 1 Answer

#### Explanation:

**CONSTANTINOPLE**

First of all just consider the pattern of vowels and consonants.

We are given

The first and last of these

That leaves us with

#{5}: 6#

#{4,1}: 6xx5 = 30#

#{3,2}: 6xx5 = 30#

#{3, 1, 1}: (6xx5xx4)/2 = 60#

#{2, 2, 1}: (6xx5xx4)/2 = 60#

#{2, 1, 1, 1}: (6xx5xx4xx3)/(3!) = 60#

#{1,1,1,1,1}: 6#

That is a total of

Next look at the subsequences of vowels and consonants in the arrangements:

The **O**'s.

The **N**'s and **T**'s

So the total possible number of arrangements satisfying the conditions is