In how many ways can we select any 4 letters | vedclass

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(C) The word $CORGOO$ contains $6$ letters: $C, O, R, G, O, O$. The distinct letters are $C, R, G, O$. The frequency is $O: 3, C: 1, R: 1, G: 1$.We ne

Vedclass · Accepted Answer

$7$

Vedclass · Answer

(C) The word $CORGOO$ contains $6$ letters: $C, O, R, G, O, O$. The distinct letters are $C, R, G, O$. The frequency is $O: 3, C: 1, R: 1, G: 1$.We need to select $4$ letters. The possible cases are:$(i)$ All $4$ letters are distinct: This is not possible as there are only $4$ distinct letters available $(C, R, G, O)$. Number of ways = $^4C_4 = 1$.$(ii)$ $2$ letters are same and $2$ are distinct: We select one pair of $O$'s $(^1C_1 = 1)$ and $2$ letters from the remaining $3$ distinct letters $(C, R, G)$. Number of ways = $1 	imes ^3C_2 = 3$.$(iii)$ $3$ letters are same and $1$ is distinct: We select the three $O$'s $(^1C_1 = 1)$ and $1$ letter from the remaining $3$ distinct letters $(C, R, G)$. Number of ways = $1 	imes ^3C_1 = 3$.Total number of ways = $1 + 3 + 3 = 7$.

In how many ways can we select any $4$ letters from the word $CORGOO$?

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