The number of four-letter words that can be formed using the letters of the word BARRACK is

Question

The number of four-letter words that can be formed using the letters of the word BARRACK is ________.

Smart Achievers · Accepted Answer

(270)

Given word : BARRACK

Case 1: If all four letters are different, then number of words $= {}^{5}C_{4} \times 4! = 120$

Case 2: If two letters are of same kind and other are different, then number of words $= {}^{2}C_{1} \times {}^{4}C_{2} \times \frac{4!}{2!} = 144$

Case 3: If first two are same and second two are also same letters, then number of words $= \frac{4!}{2! 2!} = 6$

$∴$ Total number of words $= 120 + 144 + 6 = 270$

Solution

Q.
The number of four-letter words that can be formed using the letters of the word BARRACK is ________.

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Solution

Q. The number of four-letter words that can be formed using the letters of the word BARRACK is ________.

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Q.
The number of four-letter words that can be formed using the letters of the word BARRACK is ________.