"EDUCATION" contains 9 letters in all.
Set of consonants = {C,D,N,T}
Set of vowels = {A,E,I,O,U}
Always choose the most restrictive things first. The most
restrictive things to choose here are the 1st and 6th letters,
so we choose them first.
Choose the 1st letter as a consonant in any of 4 ways.
Choose the 6th (last) letter as a vowel any of 5 ways.
There now remain only 7 letters to choose from, (for 2 have been chosen).
Choose the 2nd letter as any of the remaining letters in 7 ways.
There now remain only 6 letters to choose from.
Choose the 3rd letter as any of the remaining letters in 6 ways.
There now remain only 5 letters to choose from.
Choose the 4th letter as any of the remaining letters in 5 ways.
There now remain only 4 letters to choose from.
Choose the 5th letter as any of the remaining letters in 4 ways.
Multiply those numbers of ways together.
4*5*7*6*5*4 = 16,800
Edwin
