HELP ASAP FOR DATA MANAGEMENT QUESTION

Question

Find the number of ways of arranging the letters in the word BEACHFRONT if the second and third letters must be consonant and the last letter must be a vowel. Show all your work.



Answer 1

Arshiyanformation

There are 7 different consonants and 3 different vowels here.

So let's think about the letters where we have information.

We can choose the 2nd letter in 7 ways (as it must be a consonant).

Having chosen that there are 6 ways to choose the 3rd letter (7 consonants, one used already).

And there are 3 ways of choosing the last letter as it must be a vowel.

So we can choose the 2nd/3rd/last letter combination in 7 x 6 x 3 = 126 ways.

The other seven letters there is no restriction. We can choose the first from 7 letters (10 - 3 already used).

1st letter - we can choose from 7

4th letter - we can choose from 6

5th - choose from 5

6th - choose from 4

7th - choose from 3

8th - choose from 2

9th - choose from 1

So total ways of choosing letters = 126 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 126 x 7 ! = 635 040 ways

Mike