Question

How many 3 letter words with or without meaning can be formed out of the letters of the word ‘signature’ , if repetition of the letters is not allowed?

Answer 1

Gas
Are
Ant
Tin
Here is your answer

Answer 2

Number of 3-letter words that can be formed from the word SIGNATURE without repetition = 504

Given,

Word - SIGNATURE

Repetition is not allowed

To Find,

Number of 3 letter words that can be formed from the word SIGNATURE

Solution,

Number of words that can be formed out of a word = ⁿPr = $\frac{n!}{(n-r)!}$

where n is the number of letters available

and r is the number of letters required to form the word

In the given situation,

n = number of letters in the word SIGNATURE = 9

r = 3 (number of letter required)

Number of words = ⁹P₃

Number of words = $\frac{9!}{ 6! }$

Number of words = $\frac{9*8*7*6*5*4*3*2*1}{6*5*4*3*2*1}$

Number of words = 9 * 8 * 7

Number of words = 504

Thus, 504 3-letter words can be formed.

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