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