MBApyq

Permutations of word EXTRA

CMAT 2020 · Quantitative Techniques & Data Interpretation · Easy · Permutation and Combination

All CMAT 2020 questionsMore Permutation and Combination questionsAll CMAT QTDI

In how many different ways, can the letters of the words EXTRA be arranged so that the vowels are never together ?

  1. A.

    168

  2. B.

    48

  3. C.

    120

  4. D.

    72

Answer

D

Explanation

Total arrangements of EXTRA = 5!=1205! = 120.

Vowels in EXTRA are E and A. Treating (EA) as one block, we have 4 units: X, T, R, (EA). Arrangements with vowels together = 4!×2!=24×2=484! \times 2! = 24 \times 2 = 48.

Arrangements with vowels never together = 120−48=72120 - 48 = 72.

Related Permutation and Combination questions

Practise this under exam conditions

Sign in to solve it with a live timer, the on-screen CAT calculator, and streak and accuracy tracking across every question you attempt.

Solve in the workspace