How many different words can be formed from the letters of the word GANESHPURI if the vowels always occupy even places ?

In the word GANESHPURI, the vowels are A,E,I and U. And there are 5 even places...

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Hence the 4 vowels can occupy the 5 even places in ⁵P₄ ways. And the rest remaining 6 letters G,N,S,H,P and R can be arranged in 6! ways.

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Hence the total no. of words that can be formed from the word GANESHPURI, with vowels at even places = 6! *⁵P₄ = 6! * 5! / (5-4)! = 6! * 5! = 720 * 120 = 86,400 words

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