"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 :"

Question

Accepted Answer

"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 = ${{4!} \over {2!}}$

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

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

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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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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