Question

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In how many ways can the letters of the word RAINBOW be arranged?
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Answer 1

Answer:

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Out of 7 possible ways subract the one having either all vowel together or no vowel are together. (8) How many words are there in which first and last letters are vowels? (9) If arrangements formed are arranged in dictionary form, then what is the position of the word RAINBOW in that dictionary? Total ways of arranging the letters = 7! = 5040 ways.

Answer 2

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In how many ways can the letters of the word RAINBOW be arranged?

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• The word RAINBOW has 7 letters.
• None of the alphabets are repeated
• No condition for arrangement is given

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Therefore it can be arranged in 7! ways.

7! = 7 × 6 × 5 × 4 × 3 × 2 × 1

7! = 5040

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The letters of the word RAINBOW can be arranged in 5040 ways!

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