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Question
Find the number of permutations of n different things taken r at a time such that two specific things occur together.
Solution
A bundle of 2 specific things can be put in r places in (r – 1) ways (Why?)
And 2 things in the bundle can be arranged themselves into 2 ways.
Now (n – 2) things will be arranged in (r – 2) places in n –2Pr –2 ways.
Thus, using the fundamental principle of counting, the required number of permutations will be `2 * (r - 1) * ""^(n - 2)P_(r - 2)`.
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