Mathematics, 05.03.2021 14:00 estefaniapenalo
Five boys and five girls are seated around a table. How many ways can the seating be arranged to meet each condition? (Not meeting all conditions at once, one condition for one answer)
a) Without restriction (literally anywhere they want)
b)If the boys and girls are in alternating order (boy, girl, boy, girl, etc.)
c)If there are 5 couples, all of whom sit together
d) If all the boys sit together and all the girls sit together.
e) If four couples sit together, but Walter and Maude do not
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For every corresponding pair of cross sections, the area of the cross section of a sphere with radius r is equal to the area of the cross section of a cylinder with radius and height 2r minus the volume of two cones, each with a radius and height of r. a cross section of the sphere is and a cross section of the cylinder minus the cones, taken parallel to the base of cylinder, is the volume of the cylinder with radius r and height 2r is and the volume of each cone with radius r and height r is 1/3 pie r^3. so the volume of the cylinder minus the two cones is therefore, the volume of the cylinder is 4/3pie r^3 by cavalieri's principle. (fill in options are: r/2- r- 2r- an annulus- a circle -1/3pier^3- 2/3pier^3- 4/3pier^3- 5/3pier^3- 2pier^3- 4pier^3)
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Five boys and five girls are seated around a table. How many ways can the seating be arranged to mee...
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