Question

How many different three letter words, can be made from the letters of the word CHANGE, both with and without meaning but without any repetition?

• A. $125$
• B. $124$
• C. $120$
• D. $102$

Answer 1

The correct option is C $120$

Given word: CHANGE
Number of letters in CHANGE $=6$
So, first letter can be filled by $6$ ways.
second letter can be filled by $5$ ways.
and third letter can be filled by $4$ ways.
Hence, total number of ways
$=6\times 5\times 4=120$


Using permuation
${}^6{P}_3=\frac{6!}{(6-3)!}$
$=\frac{6!}{3!}$
$=\frac{6\times 5\times 4\times 3!}{3!}$
$=6\times 5\times 4$
$=120$