Question

The number of ways in which four letters can be selected from the word 'DEGREE' is

• A. $7$
• B. $6$
• C. $\frac{6!}{3!}$
• D. None of these

Answer 1

The correct option is A $7$

There are $6$ letters in the word 'DEGREE', namely $3\text{E's}$ and $\text{D, G, R}$. Four letters out of six can be selected in the following ways
(i) $3$ like letters and $1$ different, viz. $\text{EEE + D, G, R}$
(ii) $2$ like letters and $2$ different, viz. $\text{EEE}+$ any two of $\text{D, G, R}$.
(iii) All different letters, viz. $\text{EDGR}$.
So, the total number of ways
${=}^3{C}_1{+}^3{C}_2+1=3+3+1=7$