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- 31. In how many different ways can the letters of the word 'LETTER' be arranged?

A.128

B.160

C.180

D.150

Answer & Explanation

Answer: Option C

Explanation:**But in these 6 letters, 'E' occurs 2 times, 'T' occurs 2 times and rest of the letters are different.**

Hence, number of ways to arrange these letters = 6!/[(2!)(2!)]= 6×5×4×3×2×1/[(2×1)(2×1)] = 180

Hence, number of ways to arrange these letters = 6!/[(2!)(2!)]= 6×5×4×3×2×1/[(2×1)(2×1)] = 180

- 32. How many words with or without meaning, can be formed by using all the letters of the word, 'NARESH' using each letter exactly once?

A.360

B.480

C.600

D.720

Answer & Explanation

Answer: Option D

Explanation:**The word 'NARESH' has 6 letters and all these letters are different.**

Total words (with or without meaning) formed by using all these

6 letters using each letter exactly once

= Number of arrangements of 5 letters taken all at a time

= 6

Total words (with or without meaning) formed by using all these

6 letters using each letter exactly once

= Number of arrangements of 5 letters taken all at a time

= 6

_{P}_{6}= 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720- 33. How many arrangements can be made out of the letters of the word 'EXCELLENT' ?

A.30250

B.30246

C.30260

D.30240

Answer & Explanation

Answer: Option D

Explanation:**The word 'EXCELLENT' has 9 letters.**

But in these 9 letters, 'E' occurs 3 times,'L' occurs 2 times and rest of the letters are different.

Hence,number of ways to arrange these letters =9!/[(3!)(2!) = [9×8×7×6×5×4×3×2×1/[(3×2×1)(2×1)] = 30240

But in these 9 letters, 'E' occurs 3 times,'L' occurs 2 times and rest of the letters are different.

Hence,number of ways to arrange these letters =9!/[(3!)(2!) = [9×8×7×6×5×4×3×2×1/[(3×2×1)(2×1)] = 30240

**To whom this Permutations Questions and Answers section is beneficial?**

Students can learn and improve on their skillset for using Verbal Ability effectively and can also prepare for competitive examinations like...

- All I.B.P.S and Public Sector Bank Competitive Exam
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- Career Aptitude Test (IT Companies) and etc.