Drew's school is forming a planning committee for an upcoming cultural festival. the committee of 4 members is to be selected from among 10 teachers and 6 students. the probability that the committee contains exactly two members from each group is _?

All in all there are 16 teachers and students. The number of ways that 4 members can be selected is calculated through the use of the combination equation.

                                                n = 16C4

                                                n = 1820

The number of ways that exactly two members can be chosen from each group can be calculated the same way as above and multiplying the results. This operation is shown below.

                                                N = (10C2) x (6C2)

                                                N = 675

The probability is computed by dividing N by n.

                                    Probability = (675/1820)

                                                P = 0.37 or 37%

Thus, the probability that exactly 2 members from each group will be chosen is equal to 37%. 

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.