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(6b.) prob ( of at least one woman is on the committee) = 5C2 + 3C1/8C5+8C3 = 5!/2!(5 - 2)! + 3!/11(3 -1)!= 5!/2!3! + 3!/1!2! = 120/2X6 + 6/1X2 8!/5!(8-5)! + 8! /3!(8-5)! = 8!/5! 3! + 8!/3!3! = 40320/120X6 + 40320/6X6 = 120/12 + 6/2=10 + 3 = 13 40320/720 - 40320/36 = 56 + 1120 = 1176 (11a) f(x)=x-3/2x-1, g(x)=x-1/x-1, g of =g(f(x), g of =x-3/2x-1-1/x+3/2x-1+1, g of =x-3-(2x-1)/2x-1/x-3 +(2x-1)/2x-1, x-3-2x+1/x-3+2x-1, -x-2/3x-4 =x+2/4-3x. (11b) y=9x-x^3, y=x(9-x^2), y=x(3^2-x^2), y =x(3-x)(3+x), for the roots of y =0, y=x(3-x)(3+x)=0, =x=0,3 or -3, y=9x-x^2, dy/dx=9-3x^2, at turnin point, dy/dx=0, 9-3x^2=9, x^2=3, x=root3, x=1.732, For maximum and minimum values, when x=1.732, y=9(1.732)-(1.732)^3, =15.588-5.196, =10.392(maximum) when x=1.732 =-10.392 minimum