Ten 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 are

Solution :
Total number of words that can be formed using 5 letters out of 10 given different letters
$$ = 10 \times 10 \times 10 \times 10 \times 10$$     (as letters can repeat )
= 1,00,000
Number of words that can be formed using 5 different letters out of 10 different letters
$$ = {\,^{10}}{P_5}$$  (none can repeat)
$$ = \frac{{10!}}{{5!}} = 30,240$$
∴ Number of words in which at least one letter is repeated
= total words - words with none of the letters repeated
$$= 1,00,000 - 30,240 = 69760$$