Alicia has 6 paintings she wants to hang side by side on her wall. a) in how many ways can she arrange all 6 paintings? show your work. b) if she only wants to display 4 of the paintings, in how many ways can she choose the paintings she wishes to display? show your work. c) in how many ways can she arrange 3 out of the 6 paintings? show your work.

A) 720 ways

B) 15 ways

C) 6 ways

Step-by-step explanation:

A) To find the number of ways Alicia can arranger her 6 paintings, we will find factorial of 6 by multiplying all of the positive integers equal to or less than that number i.e. 6 to get:

6! = 6 * 5 * 4 * 3 * 2 * 1 = 720

Alicia can arrange her paintings in 720 ways.

B) We use the following formula (when order is not important) to find the number of permutations of n objects taken r at a time:

Therefore, Alicia can choose any 4 of her paintings in 15 ways.

C) Number of ways Alicia can arrange 3 out of 6 paintings = 3! = 3*2*1 = 6 ways

step-by-step explanation:

hihi so drawing these 2 triangles is fairly simple. all that's left is finding the height of each one. luckily, we have a side length and an angle, so there is a trig function we can use to solve for the height. the easiest one to use would be tangent, since we have 2/3 things needed to find and the third needed is what we are solving for. tan(73°) * 30 ~= 98.13 and tan(73°) * 35 ~= 114.45