Question

in how many ways can 3 machines be arranged out of 8 different machines​

Answer 1

$\huge{\mathcal{\purple{A}\green{N}\pink{S}\blue{W}\purple{E}\green{R}\pink{!}}}$

There are 7 letters in the given word, out of which there are 3 vowels and 4 consonants.

Let us mark out the position to be filled up as follows:

(

1

)(

2

)(

3

)(

4

)(

5

)(

6

)(

7

)

Now, the 3 vowels can be placed at any of the three places out of the four, marked 1,3,5,7.

So, the number of ways of arranging the vowels =

4

P

3

=4×3×2=24.

Also, the 4 consonants at the remaining 4 positions may be arranged in

4

P

4

=4!=24 ways.

∴ the requisitie number of ways =(24×24)=576.