The number of ways in which any four letters | vedclass

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(C) The word '$CORGOO$' contains $6$ letters: $C, O, R, G, O, O$. The distinct letters are ${C, O, R, G}$ and the frequency of '$O$' is $3$.We need to

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$7$

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(C) The word '$CORGOO$' contains $6$ letters: $C, O, R, G, O, O$. The distinct letters are ${C, O, R, G}$ and the frequency of '$O$' is $3$.We need to select $4$ letters. The possible cases are:$(i)$ All $4$ letters are different: We select $4$ letters from ${C, O, R, G}$. The number of ways is $^4C_4 = 1$.$(ii)$ $2$ letters are alike and $2$ are different: We select the pair of '$O$'s in $1$ way. Then we select $2$ more letters from the remaining $3$ distinct letters ${C, R, G}$. The number of ways is $1 	imes ^3C_2 = 3$.$(iii)$ $3$ letters are alike and $1$ is different: We select the three '$O$'s in $1$ way. Then we select $1$ letter from the remaining $3$ distinct letters ${C, R, G}$. The number of ways is $1 	imes ^3C_1 = 3$.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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