If letters of the word PENCIL are arranged in | vedclass

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Question

(C) The word $PENCIL$ contains $6$ distinct letters. The total number of ways to arrange these $6$ letters is $6! = 720$.To find the number of arrange

Vedclass · Accepted Answer

$\frac{1}{3}$

Vedclass · Answer

(C) The word $PENCIL$ contains $6$ distinct letters. The total number of ways to arrange these $6$ letters is $6! = 720$.To find the number of arrangements where $N$ is next to $E$,we treat $(NE)$ as a single unit. Now,we have $5$ units to arrange: $(NE), P, C, I, L$. These $5$ units can be arranged in $5! = 120$ ways.Within the unit $(NE)$,the letters $N$ and $E$ can be arranged in $2! = 2$ ways (i.e.,$NE$ or $EN$).Therefore,the total number of favorable arrangements is $5! 	imes 2! = 120 	imes 2 = 240$.The probability is $\frac{	ext{Favorable outcomes}}{	ext{Total outcomes}} = \frac{240}{720} = \frac{1}{3}$.

If letters of the word $PENCIL$ are arranged in random order,what is the probability that $N$ is always next to $E$?

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