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  • Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.

Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.

 

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Combination of n things taken r at a time in which 3 things always occur together=^ {n-3}C_{r-3}  

3 things taken together is considered 1 group   Number of arrangement of 3 things=3! 

Now, number of arrangement of r-2 objects=(r-2)!

Total number of arrangements=^{n-3}C_{r-3}*(r-2)!*3!

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