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### Question

The letters of the word 'BEAUTY' have to be arranged such that the vowels occupy only the odd positions. How many different ways are possible?

**A**

36.

**B**

46.

**C**

26.

**D**

56.

**Soln.**

**Ans: a**

This word has 6 letters, out of which 3 are consonants and 3 are vowels. The vowels have to occupy three fixed odd positions. We can place 3 vowels in first odd place, 2 in second odd place and 1 in the third odd place, giving 3 × 2 × 1 = 6 permutations. This will be done with the consonants also. So the total possibilities are 6 × 6 = 36.