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For the second question:

You are choosing 7 blocks. 6 have already been chosen, ie: two blue, two green, two red. So far you have: 5C2 x 4C2 x 3C2

Its only a question of choosing the last one. This may be either of the three colours, so:

Case 1: Last block is red:

5C3 x 4C2 x 3C2 = 180

Case 2: Last block is blue:

5C2 x 4C3 x 3C2 = 120

Case 3: Last block is green:

5C2 x 4C2 x 3C3 = 60

Add all the cases, you get 360

For your second question,

there are 7 block choices, and there must be 2 of each colour.

Since there must be 2 of each 6 of your blocks must stay the same, every single time

Therefore, the only block that can be different is the seventh block, the only variability is the seventh block.

There are three choices for this seventh block: red, green and blue.

Therefore there are only three ways you can select the blocks.(This is only if the order does not matter, which I assume is the case as it isn't specified in the question)

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Answers by Expert:

I can answer questions at a Calc 1 level and below, although I am a little rusty in Geometry. Anything higher than that I will not be able to help with.

I dealt with math on a daily basis for quite some time. I am a computer programmer, and use complex math frequently in the applications I have to write.**Education/Credentials**

Currently working on a double BS in Computer Science and Math. I am approximately 2/3 of the way done.