Add them:
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- \binom{6}{2} + \binom{6}{3} + \binom{6}{4} + \binom{6}{5}
- Calculate each term:
- \binom{6}{2} = 15, \quad \binom{6}{3} = 20, \quad \binom{6}{4} = 15, \quad \binom{6}{5} = 6
- + 20 + 15 + 6 = 56
- Thus, the number of valid pilot selections is \(\boxed{56}\).Question: A palynologist is analyzing spherical pollen grains under a microscope. If the radius of a pollen grain is $ r $ units, what is the ratio of the surface area of the pollen grain to the surface area of a hemispherical spore with radius $ 3r $?
- The surface area of a sphere is given by $ 4\pi r^2
