# Find the number of different 4-letter words, with or without meanings,

Question:

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

Solution:

Here, we need to permute four of the letters from the available 6 letters of the word NUMBER.

Number of different four letter words = Number of arrangements of 6 letters, taken 4 at a time =6 P4

$=\frac{6 !}{(6-4) !}$

$=\frac{6 !}{2 !}$

$=\frac{6 \times 5 \times 4 \times 3 \times 2 !}{2 !}$

$=6 \times 5 \times 4 \times 3$

= 360