Question

How many different words beginning and ending with a constant can be formed out of the word EQUATION

Answer 1

consonant, not constant...

There are 3 consonants in this word. They can be placed at both ends of a word in $\dfrac{3!}{(3-2)!}=3!=6$ ways. The remaining 5 letters can be arranged in $5!=120$ ways.

Therefore, there are $6\cdot120=720$ different words.