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6.Permutation and Combination
hard
The number of ways in which any four letters can be selected from the word ‘$CORGOO$’ is
A
$15$
B
$11$
C
$7$
D
None of these
Solution
(c) Four letters can be selected in the following ways
$(i)$ All different $i.e.$ $C,\;O,\;R,\;G$.
$(ii)$ $2$ like and $2$ different.
$(iii)$ $3$ like and $1$ different
$i.e.$ three $O$ and $1$ from $R$, $G$ and $C$.
The number of ways in $(i)$ is $^4{C_4} = 1$
The number of ways in $(ii)$ is $1\;.{\;^3}{C_2} = 3$
The number of ways in $(iii)$ is $1{ \times ^3}{C_1} = 3$
Therefore, required number of ways = $1 + 3 + 3 = $7.
Standard 11
Mathematics
