Permutations and Combinations 1 Question 10
10. The different letters of an alphabet are given. Words with five letters are formed from these given letters. Then, the number of words which have at least one letter repeated, is
(1980, 2M)
(a) 69760
(b) 30240
(c) 99748
(d) None
Analytical & Descriptive Question
Show Answer
Answer:
Correct Answer: 10. (a)
Solution:
- Total number of five letters words formed from ten different letters $=10 \times 10 \times 10 \times 10 \times 10=10^{5}$
Number of five letters words having no repetition
$$ =10 \times 9 \times 8 \times 7 \times 6=30240 $$
$\therefore$ Number of words which have at least one letter repeated $=10^{5}-30240=69760$
