Question

find the number of arrangements that can be formed by using all the letters of the word MATRIX,so that the vowels occupy even places

Answer 1

In MATRIX, number of distinct letters = 6
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Number of vowels = 2

vowels occupy only even places.

Number of even places = 3

So 2 vowels are going to be arranged in 3 places. Number of ways = 3P2 = 3! ÷ (3-2)! = 6÷1 = 6
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Number of consonants = 4

4 consonants will be arranged in the rest 4 places.

number of ways = 4P4 = 4! ÷ (4-4)! = 4! ÷ 0! = 24 ÷ 1 = 24
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total arrangements= 24 × 6 = 144