Three letters are chosen at random from the l | vedclass

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Question

(A) The word $VARIABLE$ consists of $8$ letters: $V, A, R, I, A, B, L, E$. There are $4$ consonants $(V, R, B, L)$ and $4$ vowels $(A, A, I, E)$.
Tot

Vedclass · Accepted Answer

$\frac{1}{2}$

Vedclass · Answer

(A) The word $VARIABLE$ consists of $8$ letters: $V, A, R, I, A, B, L, E$. There are $4$ consonants $(V, R, B, L)$ and $4$ vowels $(A, A, I, E)$.
Total number of ways to form a $3$-letter word from $8$ letters is $P(8, 3) = 8 	imes 7 	imes 6 = 336$.
To find the number of words with a consonant in the middle,we fix the middle position with one of the $4$ consonants. This can be done in $4$ ways.
The remaining $2$ positions can be filled by the remaining $7$ letters in $P(7, 2) = 7 	imes 6 = 42$ ways.
Total favorable words = $4 	imes 42 = 168$.
Probability = $\frac{168}{336} = \frac{1}{2}$.
Note: The calculated probability is $\frac{1}{2}$. Given the options provided,there is a discrepancy in the question's options as $\frac{1}{2}$ is not listed.

Three letters are chosen at random from the letters of the word $VARIABLE$ and all possible three-letter words (with or without meaning) are formed with them. Then the probability of getting a three-letter word having a consonant as its middle letter is

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