If P, Q, R, S are 4 individuals, how many teams of size exceeding one can be formed, with Q as a member?

The correct option is 7.

We are given a set of 4 individuals: P, Q, R, and S. We want to find the number of teams that can be formed such that:
1. The size of the team is strictly greater than one (size > 1).
2. Q must be a member of the team.

Since Q must be in every team, Q is already fixed as one member of the team. The remaining members of the team must be chosen from the other 3 individuals: P, R, and S.

Let's analyze the possible team sizes. Since the total number of individuals is 4, the maximum team size is 4. The team size must exceed one, so the allowed team sizes are 2, 3, or 4.

Case 1: Team of size 2
Q is already a member. We need to choose exactly 1 more member from the remaining 3 individuals (P, R, S).
The number of ways to choose 1 individual out of 3 is given by the combination formula:
$$\left(\genfrac{}{}{0ex}{}{3}{1}\right)=3$$
The possible teams of size 2 are: {Q, P}, {Q, R}, and {Q, S}.

Case 2: Team of size 3
Q is already a member. We need to choose exactly 2 more members from the remaining 3 individuals (P, R, S).
The number of ways to choose 2 individuals out of 3 is:
$$\left(\genfrac{}{}{0ex}{}{3}{2}\right)=3$$
The possible teams of size 3 are: {Q, P, R}, {Q, P, S}, and {Q, R, S}.

Case 3: Team of size 4
Q is already a member. We need to choose all 3 remaining individuals (P, R, S) to complete the team.
The number of ways to choose 3 individuals out of 3 is:
$$\left(\genfrac{}{}{0ex}{}{3}{3}\right)=1$$
The only possible team of size 4 is: {Q, P, R, S}.

To find the total number of teams, we sum the number of possibilities from each case:
$$\text{Total Teams}=3+3+1=7$$
Therefore, 7 such teams can be formed.