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Question
Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.
Solution
Given r places, we first fill up 3 places by 3 particular things. This can be done in rP3 ways.
Now, we have to fill remaining r − 3 places with remaining n − 3 things.
This can be done in n − 3Pr − 3 ways.
Thus, the required number of permutations will be rP3 × n − 3Pr − 3 ways.
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