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How Many Words Can Be Formed with the Letters of the Word 'University', the Vowels Remaining Together? - Mathematics

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प्रश्न

How many words can be formed with the letters of the word 'UNIVERSITY', the vowels remaining together?

उत्तर

The word UNIVERSITY consists of 10 letters that include four vowels of which two are same.
Thus, the vowels  can be arranged amongst themselves in

4!2!ways.Keeping the vowels as a single entity, we are left with 7 letters, which can be arranged in 7! ways.
By fundamental principle of counting, we get,
Number of words =  7!×4!2! = 60480

 

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Factorial N (N!) Permutations and Combinations
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 16: Permutations - Exercise 16.5 [पृष्ठ ४२]

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आरडी शर्मा Mathematics [English] Class 11
पाठ 16 Permutations
Exercise 16.5 | Q 3 | पृष्ठ ४२

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