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

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
\[= \frac{6!}{(6 - 4)!}\]
\[ = \frac{6!}{2!}\]
\[ = \frac{6 \times 5 \times 4 \times 3 \times 2!}{2!}\]
\[ = 6 \times 5 \times 4 \times 3 \]
\[ = 360\]