The number of ways in which any four letters | vedclass

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Question

(C) The word $CORGOO$ contains $6$ letters: $C, O, R, G, O, O$. The distinct letters are $C, O, R, G$. The frequency of letters is: $O$ appears $3$ ti

Vedclass · Accepted Answer

$7$

Vedclass · Answer

(C) The word $CORGOO$ contains $6$ letters: $C, O, R, G, O, O$. The distinct letters are $C, O, R, G$. The frequency of letters is: $O$ appears $3$ times,while $C, R, G$ appear $1$ time each.We need to select $4$ letters. The possible cases are:$(i)$ All $4$ letters are different: This is not possible as there are only $4$ distinct letters available $(C, O, R, G)$. Selecting all $4$ gives $1$ way.$(ii)$ $2$ letters are alike and $2$ are different: We select $2$ $O$'s (the only repeating letter) and $2$ letters from the remaining $3$ distinct letters $(C, R, G)$. The number of ways is $^3C_2 = 3$.$(iii)$ $3$ letters are alike and $1$ is different: We select $3$ $O$'s and $1$ letter from the remaining $3$ distinct letters $(C, R, G)$. The number of ways is $^3C_1 = 3$.Total number of ways = $1 + 3 + 3 = 7$.

The number of ways in which any four letters can be selected from the word $CORGOO$ is

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