JEE Main · 2021 · 20 Jul 2021 · Shift 1 · Probability

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Words with or without meaning are to be formed using all the letters of the word EXAMINATION. The probability that the letter M appears at the fourth position in any such word is :

(A) $\frac{1}{9}$
(B) $\frac{1}{11}$ ✓ Correct
(C) $\frac{2}{11}$
(D) $\frac{1}{66}$

Answer: (B)

Solution

EXAMINATION has

11

letters in which each of

A

I

and

N

occurs twice while

E

X

M

T

and

O

occur once, so the number of words is

\frac{11 !}{2 ! 2 ! 2 !}

. Holding

M

in the fourth place leaves the other ten letters, still carrying the same three pairs of repeats, to fill the remaining ten places in

\frac{10 !}{2 ! 2 ! 2 !}

ways. The required probability is

\frac{10 ! / ( 2 ! 2 ! 2 !)}{11 ! / ( 2 ! 2 ! 2 !)} = \frac{10 !}{11 !} = \frac{1}{11}

so the probability that

M

occupies the fourth position is

\frac{1}{11}

JEE Main · 2021 · 20 Jul 2021 · Shift 1 · Single correct option

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JEE Main · 2021 · 20 Jul 2021 · Shift 1 · Probability

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