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5. How many different words can be formed with the letters of word 'UNIVERSITY'so that allthe vowels occur together? |
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Answer» Answer: 60480 Step-by-step explanation: Given as The word ‘UNIVERSITY’ Here's 10 letters in the word ‘UNIVERSITY’ out of which 2 are I’s Here's are 4 VOWELS in the word ‘UNIVERSITY’ out of which 2 are I’s THEREFORE these vowels can be put TOGETHER in n!/ (p! × q! × r!) = 4! / 2! Ways Now, let us consider these 4 vowels as one letter, remaining 7 letters can be arranged in 7! Ways. Thus, the required number of ARRANGEMENTS = (4! / 2!) × 7! = (4 × 3 × 2 × 1 × 7 × 6 × 5 × 4 × 3 × 2 × 1) / (2 × 1) = 4 × 3 × 2 × 1 × 7 × 6 × 5 × 4 × 3 = 60480 |
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