All possible words (with or without meaning) | vedclass

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(D) The word '$CURVE$' has $5$ distinct letters: $C, U, R, V, E$. We form words by taking at least $2$ letters. The number of words of length $r$ is g

Vedclass · Accepted Answer

$\frac{3}{16}$

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(D) The word '$CURVE$' has $5$ distinct letters: $C, U, R, V, E$. We form words by taking at least $2$ letters. The number of words of length $r$ is given by $P(5, r) = \frac{5!}{(5-r)!}$. For $r=2$: $P(5, 2) = 5 	imes 4 = 20$. For $r=3$: $P(5, 3) = 5 	imes 4 	imes 3 = 60$. For $r=4$: $P(5, 4) = 5 	imes 4 	imes 3 	imes 2 = 120$. For $r=5$: $P(5, 5) = 5 	imes 4 	imes 3 	imes 2 	imes 1 = 120$. Total number of words = $20 + 60 + 120 + 120 = 320$. The number of $3$-letter words is $60$. Probability = $\frac{60}{320} = \frac{6}{32} = \frac{3}{16}$.

All possible words (with or without meaning) are formed by taking at least $2$ letters (all different) from the letters of the word '$CURVE$'. If a word is chosen at random from all the words thus formed,then the probability of getting a $3$-letter word is

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