Match List-I with List-II
| List-I | List-II | ||
|---|---|---|---|
| (A) | 5P4 − 5P2 | (I) | 120 |
| (B) | 15C11 − 10C4 | (II) | 2520 |
| (C) | In how many ways, the letters of the word 'STRESS' be arranged? | (III) | 100 |
| (D) | In how many ways, the letters of the word 'BANKING' be arranged? | (IV) | 1155 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A) - (III), (B) - (IV), (C) - (I), (D) - (II)
\(^{n}P_{r}\) counts arrangements and \(^{n}C_{r}\) counts selections; a word with repeated letters has \(\displaystyle\frac{n!}{p!\,q!\cdots}\) arrangements, where \(p, q, \ldots\) are the numbers of times each letter repeats.
(A) \(^{5}P_{4}-{}^{5}P_{2}\) — this matches (III) 100.
Arranging 4 of 5 things: \(^{5}P_{4}=5\times4\times3\times2=120\)
Arranging 2 of 5 things: \(^{5}P_{2}=5\times4=20\)
The difference is \(120-20=100\)
(B) \(^{15}C_{11}-{}^{10}C_{4}\) — this matches (IV) 1155.
Choosing 11 of 15 is the same as leaving out 4, so \(^{15}C_{11}={}^{15}C_{4}=1365\)
Choosing 4 of 10: \(^{10}C_{4}=210\)
The difference is \(1365-210=1155\)
(C) STRESS — this matches (I) 120.
6 letters, with S repeated 3 times: \(\displaystyle\frac{6!}{3!}=\frac{720}{6}=120\)
(D) BANKING — this matches (II) 2520.
7 letters, with N repeated twice: \(\displaystyle\frac{7!}{2!}=\frac{5040}{2}=2520\)