- In how many ways can 10 food items be divided into 2 groups to be sent to different laboratories for purity testing if there are 5 items in each group?
\[\binom{10}{5} = \frac{10 \cdot 9 \cdot 8 \cdot 7 \cdot 6}{5 \cdot 4 \cdot 3 \cdot 2 \cdot 1} = 252\]
- In how many ways can the 10 items be divided into 2 groups if there is at least 1 item in each group?
\[2^{10} - 2 = 1022\] (we donโt count an empty set and a 10-element set)