Question

How many arrangements of the letters in INSTRUCTOR have all of the following properties simultaneously? (a) The vowels appearing in alphabetical order (b) At least 2 consonants between each vowel (c) Begin or end with the 2 Ts (the Ts are consecutive)

Answer 1

480

Step-by-step explanation:

INSTRUCTOR

This is:-

I,

N

S

T T

R R

U

C

O

Vowels are - I, O, U

They are written in alphabetical order.

Both T's have to be in start or end.

Also, there must be 2 consonants between each vowel

So,

Case:1 - T T ... I _ _ ... O _ _ .. U ...

Where, ... represents the available spaces (4)

_ is the fixed spots

Case:2- .. I _ _ ... O _ _ .. U ...T T

Thus,
`2* 4* (5!)/(2!)=480`

2 is as there are 2 cases

4 is because 4 available spaces and one can go each time

`(5!)/(2!)=480` for rest alphabets in which R appear 2 times