Find the number of different 4-letter words (may be meaningless) that can

To find: 4 lettered word from letters of word NUMBERS

There are 7 alphabets in word NUMBERS.

The word is a 4 different letter word.

Formula:

Number of permutations of $n$ distinct objects among $r$ different places, where repetition is not allowed, is

$P(n, r)=n ! /(n-r) !$

Therefore, a permutation of 7 different objects in 4 places is

$P(7,4)=\frac{7 !}{(7-4) !}=\frac{7 !}{3 !}=\frac{5040}{6}=840$

Hence, they can be arranged in 840 words.