There are 8 members on a board of directors. if they must form a subcommittee of 6 members, how many different subcommittees are
1 answer:
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 />
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Answer:
50.40% probability that all 4 are different.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Desired outcomes:
4 digits, all different
For the first digit, it can be any of them, so there are 10 possible
For the second digit, it can be any of them other than the first digit. So there are 9 possible.
For the third digit, it can be any of them, other than the first and the second. So there are 8 possible.
By the same logic, 7 possible digits for the fourth. So
Total outcomes:
4 digits, each can be any of them(10 from 0 - 9).
So
Probability:
50.40% probability that all 4 are different.