Suppose we want to choose 4 colors, without replacement, from 17 distinct colors. (a) If the order of the choices is relevant, how many ways can this be done?
(b) If the order of the choices is not relevant how many ways can this be done?

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Ответ:

Gabby7047

27.02.2022

Mathematics

Option B

Difference between volume of cylinder and sphere is 79.51

Solution:

Given that,

Cylinder has a radius of 3 inches and a height of 4 inches

Volume of cylinder is given as:

$V = \pi r^2 h$

Where "r" is the radius and "h" is the height of cylinder

r = 3 inches

h = 4 inches

Substituting the value, we get

$V = 3.14 \times 3^2 \times 4\\\\V = 3.14 \times 9 \times 4 = 3.14 \times 36\\\\V = 113.04 \approx 113$

Thus volume of cylinder is 113 cubic inches

A sphere has a radius of 2 inches

Volume of sphere is given as:

$V = \frac{4}{3} \times \pi \times r^3$

Here, r = radius = 2 inches

Substituting the value, we get

$V = \frac{4}{3} \times 3.14 \times 2^3\\\\V = \frac{4}{3} \times 3.14 \times 8\\\\V = \frac{4}{3} \times 25.12\\\\V = 33.49$

Thus volume of sphere is 33.49 cubic inches

Difference between volume of cylinder and sphere

Difference = volume of cylinder - volume of sphere

Difference = 113 - 33.49 = 79.51

Thus Option B is correct

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Suppose we want to choose 4 colors, without replacement, from 17 distinct colors. (a) If the order of the choices is relevant, how many ways can this be done? (b) If the order of the choices is not relevant how many ways can this be done?