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  • If four letters are used at once, how many words, meaningful or not, can be created using the letters in the word Friday, assuming that no letter is repeated?<

If four letters are used at once, how many words, meaningful or not, can be created using the letters in the word Friday, assuming that no letter is repeated?

Option: 1

230


Option: 2

720


Option: 3

360

 


Option: 4

480


Answers (1)

The word FRIDAY is made up of 6 different letters.

The number of permutations of 6 various objects taken 4 at a time, which is given by

 ^{6}P_4 , can be formed into 4-letter words from the letters of the word Friday without any repetition of letters.

Thus, the required number of words that can be formed using 4 letters at a time is,

\begin{aligned} &{ }^6 P_4=\frac{6 !}{(6-4) !}\\\\ &{ }^6 P_4=\frac{6 \times 5 \times 4 \times 3 \times 2}{2}\\\\ &{ }^6 P_4=360 \end{aligned}

Hence, the required number of ways is 360.

 

 

Posted by

Ramraj Saini

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