Question

In how many different ways can the letters of the word machine can be arranged such that vowels comes in odd place

Answer 1

There are 3 vowels in the word machine, a, i and e. The 3 letters may be arranged in 4 positions,1,3, 5 and 7, since machine has 7 letters in it. So take the first vowel, a, and that can be arranged in 4 ways, in 4 different position. So after the first letter was placed, the next one one can be placed in 3 different positions. So the the two letteres together may be placed in 4x3=12 positions. and for each of those 12 positions we can place the last vowel in 2 ways, in the remaining 2 positions. So the total ways are 4x3x2=24

I do not know the level of the questioner’s math knowledge. The answer could have been shown by using factorials. I am a firm believer though in approaching things the simplest possible way.