a) $4M{\text{ }}2W$ or $5M{\text{ }}1W$

chosen in ${}^{10}{C_4} \times {}^9{C_2} + {}^{10}{C_5} \times {}^9{C_1}$

$ = 9828$

b) ${}^9{C_3} \times {}^8{C_1} + {}^9{C_4} = 798$

Prob $ = 798/9828 = 0.0812$

c) Albert + not $T...{\text{ }}{}^9{C_3} \times {}^8{C_2} + {}^9{C_4} \times {}^8{C_1}$

$ = 3360$

Tracey + not $A...{\text{ }}{}^9{C_4} \times {}^8{C_1} + {}^9{C_5}$

$ = 1134$

Number of ways $ = 4494$

d) $6! - 4! \times 5 \times 2$ or $6! - 5! \times 2{\text{ }}\left( { = 480} \right)$

OR $4! \times 5 \times 4$ or $4! \times {}^5{P_2}{\text{ }}\left( { = 480} \right)$

prob $ = 480/6! = 2/3{\text{ }}\left( {0.667} \right)$

OR using probabilities…as above

OR Women together $5!/4!{\text{ }}\left( { = 5} \right)$

Women not together $ = 15 - 5 = 10$

total ways $MMMMWW = 6!/4!2! = 15$

prob $ = 2/3$