Let's carefully determine the number of ways you and your friend can both be chosen as contestants from the 6 people in the front row.
1. Total people in the front row: 6 people (including you and your friend).
2. Total contestants to be chosen by the host: 3 people.
Given that you and your friend must be chosen among the 3 contestants, only one spot remains to be filled by any one of the remaining people.
3. Remaining people to choose from: After you and your friend are chosen, there are [tex]\(6 - 2 = 4\)[/tex] people left.
4. Ways to choose the remaining contestant: The last contestant can be chosen from these 4 people.
The number of ways to choose 1 person out of the remaining 4 people is given by the combination formula [tex]\(\binom{4}{1}\)[/tex], which calculates the number of ways to choose 1 item from a set of 4 items without regard to order.
[tex]\[\binom{4}{1} = 4\][/tex]
This calculation tells us there are 4 different ways to choose the last contestant among the remaining 4 people once you and your friend have already been chosen.
Therefore, the number of ways you and your friend can both be chosen is:
[tex]\[ \boxed{4} \][/tex]
So the correct answer is:
C. [tex]\(\binom{4}{1} = 4\)[/tex]
