Question

16. How many different words can be formed with the letters of the word 'RAJARAM'? In how many of

these,
(i) have two R and J always together?
(ii) being with Rand end with J?

Answer 1

(i) Take RRJ out and the rest letter is AAAM and permutation wise it should form 4! variations, may the 3As being Afirst, Asecond, and Athird. These three alone may form 3! permutations and when setting Afirst = Asecond =Athird one would have 3! sets of identical variations so 4!/3! = 4. And intuitively we can already see them: AAAM, AAMA, AMAA and MAAA. While inserting anything (in our case RRJ) back into a 4 letter queue, there are exactly 4+1 spots to insert (before every letter + behind the last letter) so for RRJ there would be 4*(4+1) variations which is 20. If considering RJR or JRR also applies to the answer, 20+20+20=60.