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

1.	Find the number of different 4-letter words (may be meaningless) that can be formed from the letters of the word ‘NUMBERS’,
Answer» 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.

Find the number of different 4-letter words (may be meaningless) that can be formed from the letters of the word ‘NUMBERS’,

Answer»

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.