Quantitative Reasoning

Permutation & Combination

Medium

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

181440

201540

182840

201840

✅ Correct Option: 1

REASONING has 9 letters, with N repeating twice and all others distinct.

Arrangements $= \dfrac{9!}{2!} = \dfrac{362880}{2} = 181440$ .

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?

2025: 22 May Shift 2

Out of 6 men and 4 women, a committee of 5 members is to be formed so that it has 2 women and 3 men. In how many different ways can it be done:

2026: 30 May Shift 2

Match List-I with List-II

List-I	List-II
(A) $^5P_4 - {^5P_2}$	(I) 120
(B) $^{15}C_{11} - {^{10}C_4}$	(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:

2026: 12 May Shift 1

A team of 3 tennis players is to be finalized from a group of 2 male and 3 female. In how many ways this can be done and how many teams which consist of 1 male and 2 female?

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: 3 June Shift 1

How many ways can 10 persons shake hands with two persons?

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

Solution

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