1. Given a group of n people. There are C(n, r) ways of forming groups of r out of n.
2. Where C(n, r)=

3. For example, given {Andy, John, Julia}. We want to pick 2 people to give a gift: we can pick {(Andy, John), (Andy, Julia), (John, Julia)}, so there are 3 ways. So we can list and count.
4. Or we could do this with the formula C(3, 2)=

5. C(8, 6)=

So there are C(8,6)=28 ways of chosing 6 out of 8 people to form the subcommittees. <span />
Simplify the following:
k - 2 (k - (2 - k)) - 2
-(2 - k) = k - 2:
k - 2 (k + k - 2) - 2
Grouping like terms, k + k - 2 = (k + k) - 2:
k - 2 ((k + k) - 2) - 2
k + k = 2 k:
k - 2 (2 k - 2) - 2
-2 (2 k - 2) = 4 - 4 k:
k + 4 - 4 k - 2
Grouping like terms, k - 4 k - 2 + 4 = (4 - 2) + (k - 4 k):
(4 - 2) + (k - 4 k)
k - 4 k = -3 k:
-3 k + (4 - 2)
4 - 2 = 2:
Answer: 2 - 3 k
Answer:
x = 28°, ∠ABC = 57°
Step-by-step explanation:
∠ABD = 2x+1
∠BCD = 33°
∠ABD = 90° (right angle)
which means that
∠ABC + <CBD = 90° (In the middle of ∠ABD)
Then, we can substitute to the equation to find x
(2x+1) + 33° = 90°
(2x+1) = 57°
2x = 56°
x = 28°
after finding x, we can find ∠ABC:
∠ABC = 2(28) + 1 = 57°
I hope this helps, have a great day! :)