Question

Different words are being formed by arranging the letters of the word ARRANGE. All the words obtained are written in the form of dictionary

The number of ways in which the consonants occur in alphabetic order is

• A. 360
• B. 105
• C. 240
• D. None of these

Answer 1

The correct option is B 105

We write the consonants in alphabetic order: $GNRR$

We cannot arrange these.

There are 5 gaps where we need to place $AAE$ i.e. $3$ objects which can be done in ${}^{3+5-1}{C}_{5-1}{=}^7{C}_4=35$ ways.

These may be arranged in $\frac{3!}{2!}=3$ ways.

Thus, total = $35\times 3=105$ ways.

Hence, (B) is correct.