Question

How many different words, with or without meaning, can be formed with the letters of the following words: a) book b) cone

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Seamus

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82 Answers

a)

The word "book" has 4 letters where 'o' is repeated twice. The formula to find the number of permutations of letters where some letters are repeated is

\frac{n!}{k_1! \cdot k_2! \cdot \ldots \cdot k_r!}

For "book":

\frac{4!}{2!} = \frac{24}{2} = 12

So, the number of different words that can be formed with the letters of "book" is 12.

b)

The word "cone" has 4 letters and all letters are distinct. The formula to find the number of permutations when all letters are distinct is:

n!

For "cone":

4! = 24

So, the number of different words that can be formed with the letters of "cone" is 24.

The word "book" has 4 letters where 'o' is repeated twice. The formula to find the number of permutations of letters where some letters are repeated is

For "book":

So, the number of different words that can be formed with the letters of "book" is 12.

b)

The word "cone" has 4 letters and all letters are distinct. The formula to find the number of permutations when all letters are distinct is:

For "cone":

So, the number of different words that can be formed with the letters of "cone" is 24.

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