1. The problem statement, all variables and given/known data There is a word given: "RAKSH" and n slips are provided. A person is free to write any one of the letters (R,A,K,S,H) in each of the slips. Repetition is allowed, i.e. for eg. one such case would be that all the 'n' slips are filled with the letter "R'. Then we begin our task: First we groups of 1 slip from n then groups of 2 slips from n then groups of3 4,5,6,7......n. Find the number of such groups formed that contain at least one of each of the letters, i.e. R,A,K,S,H! 3. The attempt at a solution I was told that its a difficult question. Here is what I think: it is obvious that groups of 1 to 4 members are useless. since there are 5 letters in RAKSH. First I consider those cases in which at least one of each letter is there: 5 slips have been fixed as RAKSH. and there are remaining n-5 slips , each have 5 options to get filled with. so is the answer 5n-5????? help me!