Quantitative Reasoning

Permutation & Combination

Medium

Match the LIST-I with LIST-II

LIST-I (Expression/Statements etc.) LIST-II (Values etc.)
A. $^5P_5 - ^{10}C_0$ I. 22
B. $^{15}C_{11} - ^{16}C_2$ II. 2520
C. If $^nP_3 = 9240$ , then find the value of n. III. 0
D. In how many ways, the letters of the word 'BANKING' be arranged? IV. 1245

Choose the correct answer from the options given below:

LIST-I (Expression/Statements etc.)	LIST-II (Values etc.)
A. $^5P_5 - ^{10}C_0$	I. 22
B. $^{15}C_{11} - ^{16}C_2$	II. 2520
C. If $^nP_3 = 9240$ , then find the value of n.	III. 0
D. In how many ways, the letters of the word 'BANKING' be arranged?	IV. 1245

A-I, B-II, C-III, D-IV

A-II, B-III, C-IV, D-I

A-III, B-IV, C-I, D-II

A-IV, B-I, C-II, D-III

✅ Correct Option: 3

B: $^{15}C_{11} - {}^{16}C_2 = 1365 - 120 = 1245$ , so B-IV.

C: $n(n-1)(n-2) = 9240 = 22 \times 21 \times 20$ , so $n = 22$ , giving C-I.

D: BANKING has 7 letters with N twice, so $\frac{7!}{2!} = 2520$ , giving D-II.

By elimination A-III.

Note: As printed, $^5P_5 - {}^{10}C_0 = 119$ , which is not listed; we have matched A by elimination.

2025: 29 May Shift 1

In how many different ways can the letters of the word 'DELETE' be arranged?

2025: 22 May Shift 1

How many ways can a committee of 3 people be chosen out of 7 people?

2026: 6 June Shift 1

In how many different ways can the letter of the word "DIGEST" be arranged so that the vowels are at the two ends?

2026: 26 May Shift 1

In how many different ways can the letters of the word "MANAGEMENT" be arranged?

2025: 13 May Shift 1

Match List-I with List-II

List-I	List-II
(A) $^8P_3 - ^{10}C_3$	(I) 6
(B) $^8P_5$	(II) 21
(C) $^nP_4 = 360$ , then find n.	(III) 216
(D) $^nC_2 = 210$ , find n.	(IV) 6720

Choose the correct answer from the options given below:

2025: 14 May Shift 1

There is a match between two teams. Each team has a total of 15 players. After the match, all the players of one team shake hands with all the players of the other team. What is the number of possible hand shakes?

Solution

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