Simple permutation math urgent help requested.

Question

Determine how the letters of the word ‘Equation’ can be arranged by placing the consonants in odd places?

(I know the answer 2880, I need to know how to do this type of maths, please show step by step)

Answer 1

There are 5 vowels and 3 consonants, and 4 even and 4 odd places

As the consonants are in odd places, and there are 4 odd places, the consonants can be in C(4,3) places - or C(4,1) places for the vowel - = 4, and the consonants can be in 3! orders.

Then, one of the five vowels is in the remaining odd place, and the remaining 4 vowels can be arranged among the evens in 4! ways.

C(4,3)*3!*5*4! = 4 * 6 * 5 * 24 = 2880