No. of vowels in the word THERAPY = 2 i.e. E and A In such cases we treat the group of two vowels as one entity or one letter because they are supposed to always come together. Thus, the problem reduces to arranging 6 letters i.e. T, H, R, P, Y and EA in 6 vacant places. No. of ways 6 letters can be arranged in 6 places = 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720 But the vowels can be arranged themselves in 2 different ways by interchanging their position. Hence, each of the above 720 arrangements can be written in 2 ways. ∴ Required no. of total arrangements when two vowels are together = 720 × 2 = 1440 Total no. of arrangements of THERAPY = 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040 No. of arrangement when vowels do not come together = 5040 – 1440 = 3600