What are the number of ways in which $(p + q)$ dissimilar objects can be partitioned into two groups consisting of $p$ and $q$ objects respectively is, where $p \neq q$ ?

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Solution

So,if we put any $^{'} p^{'}$ objects in $1$ group automatically we will have another group with $^{'} q^{'}$ objects.
Hence, no. of ways $=^{p + q} C_{p} =^{p + q} C_{q}$

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