7. There are seven clarinet players in the concert band. In how
many ways can they be seated in seven chairs at a concert?
Use the Fundamental Counting Principle.
A. 5,040
C. 840
B. 2,520
D. 210

Step-by-step explanation:

The number of people in the cabinet is 7.

n = 7.

Fundamental Counting Principle states that if there are m ways of doing a thing and there are n ways of doing other thing then there are total m*n ways of doing both things.

now using fundamental Counting Principle.

since 7 players can sit on chair in

7 , 6, 5 , 4, 3 , 2, 1 ways then together they can be seated in

7 * 6 * 5 * 4 * 3 * 2 * 1 ways = 5,040 ways.

To arrange this seven people in a straight cabinet, the number of way to arrange them is n!

Then,

n! = 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040.

There are 5040 ways of arranging them.

Option A is correct.

easy math just plug in a and b

step-by-step explanation:

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.