Question

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

Answer 1

Answer:

the number of 3-letter words (with or without meaning) formed by using these letters = 10P3=10×9×8=720.

Answer 2

Given,

The word SIGNATURE

To find,

The number of  3 letter words with or without meaning can be formed

Solution,

The word SIGNATURE has 9 different letters.

3 Letters out of 10 can be selected in  ¹⁰C₃ ways and then 3! Letters can be arranged in 3 Ways to form a word

The number of 3-letter words that can be formed = 3! x 10!/(7! x 3!)

= 10!/7!

= 10 x 9 x 8

= 720

Thus, 720 three-letter words can be formed from the word SIGNATURE