• # question_answer The number of different words that can be formed out of the letters of the word 'MORADABAD' taken four at a time is A) 500B) 600C) 620D) 626

In MORADABAD, we have 6 different types of letters $3{{A}^{s}}$,$2{{D}^{s}}$ and rest four different. We have to form words of 4 letters. (i) All different $^{6}{{P}_{4}}=6\times 5\times 4\times 3=360$. (ii) Two different two alike $^{2}{{C}_{1}}{{\times }^{5}}{{C}_{2}}\times \frac{4\ !}{2\,\,!}=240$ (iii) 3 alike 1 different $^{1}{{C}_{1}}{{\times }^{5}}{{C}_{1}}\times \frac{4\ !}{3\ !}=20$ (iv) 2 alike of one type and 2 alike of other type $^{2}{{C}_{2}}\times \frac{4\ !}{2\ !\ 2\ !}=6$ Therefore total number of words $=360+240+20+6=626$.