find the no. of 6 letter words that can be formed using letters of the word SQUARE such that U and A always appear together.

S Q UA R E. Ordinarily, 6 letters would give you 6! = 720 permutations. But since you want the letters "UA" always together, then as Melody often says, "rope them together", or consider them as one letter. So, instead of having 6 letters or 6! permutations, you will simply have 5! = 120 permutations.