# How many two letter words can be formed using letters from the word SPACE, when repetition of letters is allowed? - Mathematics and Statistics

Sum

How many two letter words can be formed using letters from the word SPACE, when repetition of letters is allowed?

#### Solution

Two-letter word is to be formed out of the letters of the word 'SPACE'.

Number of letters in the word 'SPACE' = n = 5

When repetition of the letters is allowed

First letter can be selected in 5 ways = ""^5"C"_1 = (5!)/(5!(5 - 1)!) = 5

Second Letter can be selected in 5 ways (as repetition is allowed the letters selected before is also available) = ""^5"C"_1 = (5!)/(5!(5 - 1)!) = 5

∴ By using the fundamental principle of multiplication,

The total number of 2-lettered words = 5 × 5 = 25.

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Chapter 6: Permutations and Combinations - Exercise 6.1 [Page 73]

#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 6 Permutations and Combinations
Exercise 6.1 | Q 4. (i) | Page 73
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