Mathematics - Permutation & Combination Question with Solution | TestHub

(i) Single letter is used, then no. of words $=5$ (ii) Two distinct letters are used, then no. of words ${}^5{\mathrm{C}}_2\times \left(\frac{6!}{2!4!}\times 2+\frac{6!}{3!3!}\right)=10(30+20)=500$ (iii) Three distinct letters are used, then no. of words ${}^5{\mathrm{C}}_3\times \frac{6!}{2!2!2!}=900$ Total no. of words $=1405$