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Find the Number of Permutations of N Distinct Things Taken R Together, in Which 3 Particular Things Must Occur Together. - Mathematics

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

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Given r places, we first fill up 3 places by 3 particular things. This can be done in rPways.
Now, we have to fill remaining r − 3 places with remaining − 3 things.
This can be done in n − 3Pr − 3 ways.
Thus, the required number of permutations will be rP3 × n − 3Pr − 3 ways.

Concept: Factorial N (N!) Permutations and Combinations
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RD Sharma Class 11 Mathematics Textbook
Chapter 17 Combinations
Exercise 17.3 | Q 4 | Page 23
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