Match the List-I with List-II
| List-I | List-II | ||
|---|---|---|---|
| (Letter Word) | (Arrangement of the letters of the word in different ways) | ||
| A. | PRESENT | I. | 181440 |
| B. | APTITUDE | II. | 4989600 |
| C. | REASONING | III. | 2520 |
| D. | MATHEMATICS | IV. | 20160 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → A - III, B - IV, C - I, D - II
The letters of an \(n\)-letter word can be arranged in \(n!\) ways if all are different. When a letter repeats, swapping the copies gives no new word, so \(n!\) is divided by the factorial of each repeat count: \(\displaystyle\frac{n!}{p!\,q!\ldots}\).
(A) PRESENT — this matches (III) 2520. 7 letters, with E twice:
Number of arrangements: \(\displaystyle\frac{7!}{2!}=\frac{5040}{2}=2520\)
(B) APTITUDE — this matches (IV) 20160. 8 letters, with T twice:
Number of arrangements: \(\displaystyle\frac{8!}{2!}=\frac{40320}{2}=20160\)
(C) REASONING — this matches (I) 181440. 9 letters, with N twice:
Number of arrangements: \(\displaystyle\frac{9!}{2!}=\frac{362880}{2}=181440\)
(D) MATHEMATICS — this matches (II) 4989600. 11 letters, with M, A and T twice each:
Number of arrangements: \(\displaystyle\frac{11!}{2!\,2!\,2!}=\frac{39916800}{8}=4989600\)