Match List-I with List-II.
| List-I | List-II |
| (A) \(^9P_2\) | (I) 30 |
| (B) \(^9C_3\) | (II) 84 |
| (C) The number of diagonals of a heptagon (a polygon with 7 sides) | (III) 14 |
| (D) The number of ways in which all the letters of the word LEVEL can be arranged (each letter used once, the two L’s identical and the two E’s identical) | (IV) 72 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A)-(IV), (B)-(II), (C)-(III), (D)-(I)
\(^nP_r\) counts arrangements, the product of \(r\) numbers counting down from \(n\); \(^nC_r\) counts selections, \(\frac{n!}{r!\,(n-r)!}\). Each List-I item is worked out with these.
(A) \(^9P_2\) — this matches (IV) 72.
\(^9P_2=9\times8=72\)
(B) \(^9C_3\) — this matches (II) 84.
\(\displaystyle ^9C_3=\frac{9\times8\times7}{3\times2\times1}=84\)
(C) The number of diagonals of a heptagon — this matches (III) 14.
Joining any 2 of the 7 corners gives a line: \(\displaystyle ^7C_2=\frac{7\times6}{2}=21\)
7 of these lines are the sides, the rest are diagonals: \(21-7=14\)
(D) The number of ways in which all the letters of the word LEVEL can be arranged — this matches (I) 30.
LEVEL has 5 letters with L twice and E twice
Arrangements \(\displaystyle =\frac{5!}{2!\times2!}=\frac{120}{4}=30\)