Discussion
In a group containing 6 cows and 4 buffalos, 4 livestock are to be selected in such a way that at least 1 cow should always be present. How many way of doing that are possible?
Answer: A
There are ten animals in all. "At least one cow" is easiest through the complement.
\[ \text{total} = {}^{10}C_{4} = 210 \]
\[ \text{no cow} = {}^{4}C_{4} = 1 \]
\[ 210 - 1 = 209 \]
With only four buffalos there is exactly one all-buffalo selection, which is what makes the complement so small.
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