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Home » How many words can be formed from the letters of the word ‘SERIES’ which start with S and end with S?
How many words can be formed from the letters of the word ‘SERIES’ which start with S and end with S?
CBSE | Class 11 | Exercise 16.5 | Maths | Permutations | RD Sharma
How many words can be formed from the letters of the word ‘SERIES’ which start with S and end with S?

Given:

The word

    \[SERIES\]

There are

    \[6\]

letters in the word

    \[SERIES\]

out of which

    \[2\]

are

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

and the rest all are distinct.

Now, Let us fix

    \[5\]

letters at the extreme left and also at the right end. So we are left with

    \[4\]

letters of which

    \[2\text{ }are\text{ }Es\]

These

    \[4\]

letters can be arranged in

    \[n!/\text{ }\left( p!\text{ }\times \text{ }q!\text{ }\times \text{ }r! \right)\text{ }=\text{ }4!\text{ }/\text{ }2!\]

Ways.

Required number of arrangements is

    \[=\text{ }4!\text{ }/\text{ }2!\]

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

    \[=\text{ }4\text{ }\times \text{ }3\]

So,

    \[=\text{ }12\]

Hence, a total number of arrangements of the letters of the word

    \[SERIES\]

in such a way that the first and last position is always occupied by the letter

    \[S\text{ }is\text{ }12\]

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