How many two-letter words can be formed using letters from the word SP

1.	How many two-letter words can be formed using letters from the word SPACE, when repetition of letters (i) is allowed (ii) is not allowed
Answer» A two-letter word is to be formed out of the letters of the word SPACE. (i) When repetition of the letters is allowed 1st letter can be selected in 5 ways. 2nd letter can be selected in 5 ways. ∴ By using the fundamental principle of multiplication, the total number of 2-letter words = 5 × 5 = 25 (ii) When repetition of the letters is not allowed 1st letter can be selected in 5 ways. 2nd letter can be selected in 4 ways. ∴ By using the fundamental principle of multiplication, the total number of 2-letter words = 5 × 4 = 20

How many two-letter words can be formed using letters from the word SPACE, when repetition of letters (i) is allowed (ii) is not allowed

Answer»

A two-letter word is to be formed out of the letters of the word SPACE.

(i) When repetition of the letters is allowed 1st letter can be selected in 5 ways. 2nd letter can be selected in 5 ways.

∴ By using the fundamental principle of multiplication,

the total number of 2-letter words = 5 × 5 = 25

(ii) When repetition of the letters is not allowed 1st letter can be selected in 5 ways. 2nd letter can be selected in 4 ways.

∴ By using the fundamental principle of multiplication,

the total number of 2-letter words = 5 × 4 = 20