Question

The number of ways in which any four letters can be selected from the word $\text{'}\mathrm{CORGOO}\text{'}$ is?

• A. $15$
• B. $11$
• C. $7$
• D. None of these

Answer 1

The correct option is C

$7$

Explanation for correct option

There are $3$ O's, $1$ C, $1$R and $1$ G

Number of ways of selecting each of the one letter is $1$ (with one O)

Now, if we select two O's and two of any other letter, then number of ways $={}^{3}C_2=3$

Now, if we choose three O's and any one of the three letters, then number of ways $={}^{3}C_1=3$

Therefore, total number of ways of selecting any four letters $=1+3+3=7$

Hence, option C is correct