Question

w many four letter words can be formed using the letters of the word "ROAMING"?
750
840
720
650
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Answer 1

Given: the word ROAMING

To find: how many four letter words can be formed using the letters of the word ROAMING

Solution:

• There are 7 letters in the word "ROAMING".

• Clearly each of the different permutations of the given seven letters taken four at a time, will give different words.

• So the required number of words is
• ${}^{7}P_{4}=\frac{7!}{(7-4)!}$
• $\quad\quad=\frac{7!}{3!}$
• $\quad\quad=\frac{7\times 6\times 5\times 4\times 3!}{3!}$
• $\quad\quad=840$

Answer: Option (B) 840 words can be formed.