• # question_answer 10 different letters of english alphabet are given words of 5 letters are formed from these given letters. How many words are formed when at least one letter is repeated? A)  69760                   B)  2912                 C)  98748                   D)  987147

Idea Here, number of permutation of n dissimilar things taken r at a time ${{=}^{n}}{{p}_{r}}=\frac{n!}{(n-r)!}$repetition is not allowed total ways $={{n}^{r}}$Number of 5 letters word if at least one letter is repeated is equal to = Total possible 5 letters word Number of 5 letters word when repetition is not allowed $={{10}^{5}}-10\times 9\times 8\times 7\times 6$ $={{10}^{5}}-30240$ $=69760$ TEST Edge Fundamental theorem of permutation and their application based questions are asked. To solve such type of question, students are advised to understand the concept of fundamental theorem.