JEE Main · 2023 · 13 Apr 2023 · Shift 2 · Permutations and Combinations

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All words, with or without meaning, are made using all the letters of the word MONDAY. These words are written as in a dictionary with serial numbers. The serial number of the word MONDAY is

(A)327✓ Correct
(B)326
(C)328
(D)324

Answer: (A)

Solution

Arranged alphabetically the letters are

A, D, M, N, O, Y

. Words beginning with

A

or with

D

number

5! + 5! = 240

. With

M

fixed first, the second letters

A, D, N

each give

4! = 24

words, contributing

72

. With

M O

fixed, the third letters

A, D

each give

3! = 6

words, contributing

12

; with

M O N

fixed, the fourth letter

A

gives

2! = 2

words. Thus

240 + 72 + 12 + 2 = 326

words precede

M O N D A Y

, so its serial number is

326 + 1 = 327

JEE Main · 2023 · 13 Apr 2023 · Shift 2 · Single correct option

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