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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 />
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 />
The length of a segment is the distance between its endpoints.
- AB and CD are not congruent
- AB does not bisect CD
- CD does not bisect AB
<u>(a) Length of AB</u>
We have:
The length of AB is calculated using the following distance formula
So, we have:
Simplify
<u>(b) Are AB and CD congruent</u>
First, we calculate the length of CD using:
Where:
So, we have:
By comparison
Hence, AB and CD are not congruent
<u>(c) AB bisects CD or not?</u>
If AB bisects CD, then:
The above equation is not true, because:
Hence, AB does not bisect CD
<u>(d) CD bisects AB or not?</u>
If CD bisects AB, then:
The above equation is not true, because:
Hence, CD does not bisect AB
Read more about lengths and bisections at: