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6. You decide to redecorate your house and you go shopping with your best friend. You may choose from the following items: three different types of sofas, four different types of tables, and two different types of rugs. In how many different ways can you choose two items if you do not want to purchase more than one type in each category? Explain your reasoning. [3T,1C]


7. How many ways can you distribute ALL 6 halloween candies among three people if each person gets at least one candy? There are many strategies you could use to get the answer. Show work. [2T,1C]



Answer :

jcherry99

Answer:

Answer to 6 = 26

Answer to 7 = 10

Step-by-step explanation:

Six

Givens

Sofas = 3

Tables = 4

Rugs = 2

Formula

I don't think there is a formula for this. You can only list the possibilites I think.

Solution

Rugs and Sofas: are chosen. Rugs * Sofa = 2 * 3 =   6

Rugs and Tables, are chosen. Rugs*Tables = 2 *4 = 8

Tables and Sofas are chosen. Tables*Sofas = 4*3 = 12

Total number of ways of choosing 2of 3  = 26

Seven

Again, I don't see any other way of doing this than by listing the possibilities.

Solution

The most any one person can get is 4. The other two get 1 each.

411

141

114              Total 3

Then the next possibility is one person gets 3 and the other 2 get one or two each.

321

312

132

123

231

213               Total 6

Now we can have 222

So the total number of ways is 10

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