Number of ways in which any four letters can be selected from word ‘ CORGOO ’ is

English

Gujarati

Hindi

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

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