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QJEEM20Ma2a65: JEE Main 2020 Mathematics - Class 11 JEEM20Ma2a65 Solution: The number of words, with or without meaning, that can be…

The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word ’SYLLABUS’ such that two letters are distinct and two letters are alike, is :

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In 'SYLLABUS' word

1. Two S letters

2. Two L letters

3. One Y letter

4. One A letter

5. One B letter

6. One U letter

Number of ways we can select two alike letters = 2C1

Then number of ways we can select two distinct letters = 5C2

Then total arrangement of selected letters = 4!2!{{4!} \over {2!}}

So total number of words, with or without meaning, that can be formed

= 2C1 ×\times 5C2 ×\times 4!2!{{4!} \over {2!}} = 240

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