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Home » Find the number of words formed by permuting all the letters of the following words : (i)ARRANGE (ii) INDIA
Find the number of words formed by permuting all the letters of the following words : (i)ARRANGE (ii) INDIA
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)ARRANGE (ii) INDIA

(i) 

    \[ARRANGE\]

There are

    \[7\]

letters in the word

    \[ARRANGE\]

out of which

    \[2\text{ }are\text{ }As,\text{ }2\text{ }are\text{ }Rs\]

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

    \[=\text{ }7!\text{ }/\text{ }\left( 2!\text{ }2! \right)\]

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

Or,

    \[=\text{ }7\times 6\times 5\times 3\times 2\times 1\]

    \[=\text{ }1260\]

 

(ii) 

    \[INDIA\]

There are

    \[5\]

letters in the word

    \[INDIA\]

out of which

    \[2\text{ }are\text{ }Is\]

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

    \[=\text{ }5!\text{ }/\text{ }\left( 2! \right)\]

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

Or,

    \[=\text{ }5\times 4\times 3\]

    \[=\text{ }60\]

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