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Home » Find the number of words formed by permuting all the letters of the following words : (i) SERIES (ii) EXERCISES
Find the number of words formed by permuting all the letters of the following words : (i) SERIES (ii) EXERCISES
CBSE | Class 11 | Exercise 16.5 | Maths | Permutations | RD Sharma
Find the number of words formed by permuting all the letters of the following words : (i) SERIES (ii) EXERCISES

(i) 

    \[SERIES\]

There are

    \[6\]

letters in the word

    \[SERIES\]

out of which

    \[2\text{ }are\text{ }Ss,\text{ }2\text{ }are\text{ }Es\]

and the rest all are distinct.

So by using the formula,

    \[n!/\text{ }\left( p!\text{ }\times \text{ }q!\text{ }\times \text{ }r! \right)\]

total number of arrangements

    \[=\text{ }6!\text{ }/\text{ }\left( 2!\text{ }2! \right)\]

    \[=\text{ }\left[ 6\times 5\times 4\times 3\times 2\times 1 \right]\text{ }/\text{ }\left( 2!\text{ }2! \right)\]

Or,

    \[=\text{ }6\times 5\times 3\times 2\times 1\]

    \[=\text{ }180\]

(ii) 

    \[EXERCISES\]

There are

    \[9\]

letters in the word

    \[EXERCISES\]

out of which

    \[3\text{ }are\text{ }Es,\text{ }2\text{ }are\text{ }Ss\]

and the rest all are distinct.

So by using the formula,

    \[n!/\text{ }\left( p!\text{ }\times \text{ }q!\text{ }\times \text{ }r! \right)\]

total number of arrangements

    \[=\text{ }9!\text{ }/\text{ }\left( 3!\text{ }2! \right)\]

    \[=\text{ }\left[ 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1 \right]\text{ }/\text{ }\left( 3!\text{ }2! \right)\]

Or,

    \[=\text{ }\left[ 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1 \right]\text{ }/\text{ }\left( 3\times 2\times 1\times 2\times 1 \right)\]

    \[=\text{ }9\times 8\times 7\times 5\times 4\times 3\times 1\]

So,

    \[=\text{ }30240\]

i

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