Question

Find the number of different 4-letter words, with or without meanings, that can be formed from the letters of the word 'NUMBER'.

Answer 1

The number of letters = 6
$\therefore$ Total number of words
= Number of arrangements of 6 letters, taken 4 at a time = $6_{P_4}$
= $\frac{6!}{(6-4)!}[\because \underset{r}{\stackrel{n}{P}}=\frac{n!}{(n-r)!}]$
= $\frac{6!}{2!}$
= $\frac{6\times 5\times 4\times 4\times 3\times 2\times 1}{2!}$
= 360
Hence, the total number of 4 digit numbers are 360.