1. Set up the expression to select exactly 2 men and the remaining 4 members from the women

Since the committee requires exactly 2 men (out of 6), the remaining $6 - 2 = 4$ members must be women (out of 5).

$\text{Number of ways} = {^6C_2} \times {^5C_4}$

2. Evaluate the combinations to find the total number of ways

$= 15 \times 5 = 75$

1. Set up the expression using the complement method by subtracting the number of ways to form a committee with no sisters from the total number of unrestricted ways.

$\text{Number of ways} = \binom{11}{6} - \binom{8}{6}$

2. Evaluate the combinations to calculate the final number of ways.

$\text{Number of ways} = 462 - 28 = 434$

1. Determine the number of ways to form a block consisting of the two sisters and exactly one man between them.

There are $3$ men to choose from to sit between the sisters, so there are $\binom{3}{1} = 3$ choices.
For any chosen man, the two sisters can swap places around him in $2! = 2$ ways.
Number of ways to form this block = $3 \times 2 = 6$.

2. Treat the block as a single unit and arrange it with the remaining people around the round table.

The block counts as $1$ unit. The remaining people ($2$ men and $1$ woman) count as $3$ units.
Total units to arrange in a circle = $1 + 3 = 4$.
Number of ways to arrange $4$ units in a circle = $(4 - 1)! = 3! = 6$.
Total possible arrangements = $6 \times 6 = 36$.

1. Seat the two sisters, fixing the circular arrangement

Since it is a circular table, we can fix the position of one sister (e.g., Sue) to remove the rotational symmetry, which gives $1$ way.
The other sister (Suzy) must be seated directly opposite her, giving only $1$ choice for her seat.

2. Arrange the remaining people

The remaining $4$ people (Muthu, Mark, Michael, and Wina) can be arranged in the $4$ remaining distinct seats in $4!$ ways.
Total number of possible arrangements $= 1 \times 1 \times 4! = 24$