Question

Ten different letters of an alphabet are given, Words with five letters are formed from these given letters. The number of words which have at least one of their letter repeated is

• A. 69760
• B. 30240
• C. 99748
• D. none of these

Answer 1

Answer: (A)

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 $=10^{5}-30240=69760$