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प्रश्न
Find the number of permutations of n different things taken r at a time such that two specified things occur together?
उत्तर
We have n different things.
We are to select r things at a time such that two specified things occur together.
Remaining things = n - 2
Out of the remaining (n - 2) things, we can select (r - 2) things in n- 2Cr -2ways.
\[ = 2 \left( r - 1 \right)^{n - 2} C_{r - 2} \times \left( r - 2 \right)!\]
\[ = 2 \left( r - 1 \right)^{n - 2} P_{r - 2}\]
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