In how many ways can the letters in PRECISION be arranged? In how many of these arrangements do the vowels occupy even places ?
No of letters in PRECISION = 9
No of ways the letters in PRECISION can be arranged = 9!/2! = 181440
No of vowels in the word PRECISION = 4
No of even spaces in the word PRECISION = 4
Vowels in even spaces = 4C4
Remaining num of letters = 5P5
4 vowels with I repeated.
Number of ways 4 vowels can occupy 4 even spaces = 4P4 / 2! (as I is repeated) = 12
Number of ways 5 consonants can occupy 5 odd spaces = 5P5 = 120
Therefore total number of ways = 12 * 120 = 1440
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