How many arrangements of the letters of the word OLYMPIC are possible if the C and the L are to be together in any order? Ans: Okay, here's one approach. OLYMPIC has 7 letters - call them 7 units. Since C and L have to be together, consider them as a single unit. So now we have 6 units to arrange. How many ways? Think of it as putting 6 units into 6 slots. The first slot can be filled in 6 ways, since you can choose any unit. The 2nd slot can be filled in 5 ways, since you have only 5 units left and can choose any unit from that. Similarly, 3rd slot can be filled in 4 ways and so on. So, the 6 slots can be filled i.e. the 6 units can be arranged, in 6*5*4*3*2*1 (aka 6! or factorial 6) ways. Which isarrangements. Now here's the catch - for each of these arrangements, the 2 letters C and L can be arranged in 2 ways (CL and LC) - they are 2 different arrangements, but the two are still together so it is a valid one. So the total number of arrangements of the 7 letters, keeping C and L together, is 720 * 2 = 1440. Hope you got it :)