In how many ways the letters of the word ldquo UNDERDOG rdquo can be arranged such that the first an...........

Quantitative Aptitude ( CCS) Permutation & Combination

In how many ways the letters of the word “UNDERDOG” can be arranged such that the first and last letters are same and no two vowels are together?

132

144

None of these

U, N, R, O, G, E and D (2 times) For first and last letter to be same First and last letter should be D

D _________________D

N R G

Now in the middle six letters no two vowels should be together So first we arrange three consonants, ways = 3!

Now from the four available spaces we select three places and then arrange the three vowels there. Ways = ⁴C₃ × 3!

Total ways = 3! × ⁴C₃ × 3! = 144

Hence, option D is correct.

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