Help due next hour!?

Question

1. Given a small department with 7 members, how many subsets of the department (containing at least one person) could be created to work on any given project?

2. A small furniture maker allows customers to choose from 3 different finishes (light, medium and dark), 4 different woods (teak, birch, pine and oak) and 6 different styles of hardware to customize an entertainment center. Given these possibilities, how many different entertainment centers can be created?

Answer 1

PROBLEM 1:

Here they are asking for the number of ways to create a unique subset of the 7 member department.

The easiest way I find to think about it is to imagine going to each person and saying "yes" or "no" they are in the subset.

There are thus 2 choices for each person (in or out). That would be 2 x 2 x 2 x 2 x 2 x 2 x 2 subsets (2^7 = 128).

However, they said you can't have the empty set (nobody selected), so you have to subtract one.

The answer is 127 subsets of 7 people are possible

PROBLEM 2:

Assuming you can only have one finish, one wood, one style, it would just be the product of the choices:

You have:
3 choices of finish
4 choices of wood
6 choices of style

3 x 4 x 6 = 72 combinations

Answer 2

1. Ok for this, take each number that goes before 7 and see how many times it goes into 7. Then add them all up.
Sooo, 1 (7 times) 2 (3 times) 3(2 times) 4,5,6,7 (1 time)
7+3+2+1+1+1+1= 10+6=16 subsets or dpts.

2. These are easy, don't even look at what they are, just look at the numbers, and multiply ! 3 * 4 * 6= 24 * 3= 72 different entertainment centers.

Answer 3

1. You want all possible combinations for 1,2,3,4,5,6,7 people.
7C1 = 7, 7C2=7*6/2*1 = 21, 7C3 = 7*6*5/3*2*1 = 35, 7C4 = 7*6*5*4/4*3*2*1 = 35, 7C5=21, 7C6=7, 7C7=1
Add all these together
7+21+35+35+21+7+1=127

2. Multiply
3*4*6 = 72

Answer 4

1) all the possible subsets are 2^7, so you do not want the empty subset, therefore it is 2^7 - 1

2) 3*4*6

Answer 5

1) 7! = 7x6x5x4x3x2x1= 5040

2) 3x4x6 = 72

Answer 6

1. Anywhere from one to seven sub-departments could be created. They're asking for the maximum, so the answer is 7.

2. Multiply all the numbers together.

3*4=12
12*6=72

Answer: 72 entertainment centers

Answer 7

I would have to agree with Puzzeling's answer.
1. 127 (It isn't 7 because it askes for all that could be created, not the max that could be created simultaniously.)
2. 72

Please remember that you shouldn't rely on Y.A. to get your homework in on time. Manage your time wisely and don't cheat yourself!

Good luck!

Answer 8

2z - 4(9 - 3z) = sixty two....amplify: 2z - 36 + 12z = sixty two, so 14z = ninety 8, so z = ninety 8/14, so z = 7. -34 = 3-D + 8/3.........multiply thro` by using 3: -102 = 9d + 8, so -a hundred and ten = 9d, so d = -a hundred and ten/9. wish this helps, Twiggy.

Answer 9

1. don't know
2. 72?