Subject: Permutations and Multiplication Principle

Name: Candice
Who is asking: Student
Level: All


  1. A forester selects 4 pink and 4 white dogwoods. The trees are to be planted in row. If a tree is distinguished by color only, in how many ways can the eight dogwoods be planted? How many of these arrangements have at least two trees of the same color side by side?
    I found the number of possibilities to be 576 (4x3x2x1x4x3x2x1), but I don't know how to find the second answer.
  2. A study is being designed to investigate the effect of polymer type, temperature, radiation dose, radiation dose rate, and pH on the ability to remove trace quantities of benzene from water. There are 2 polymer types (A and B), 3 temperatures (high, medium, low), 3 radiation doses, 3 radiation dose rates and 3 pH levels (acidic, basic, neutral).

    a) If each experimental condition is to replicated 5 times how many experimental runs must be made?
    b)How many runs are made with polymer B at high or medium temperature and low pH?

    For a) I got 810 - number of possible conditions x 5.
    And for b) I got 1x2x1x3x3 = 18. Is this correct?

Thank you in advance.

Hi Candice,

Start out with 2 pink and 2 white dogwoods. You get only 6 possibilities:

Does that agree with your formula?

I think you should see that it is 8C4, "8 choose 4" (why?) which I think is 70 - check it out.

For the second answer, try to list all the possible arrangements with NO two trees of the same colour side by side.

Question 2 part a) looks correct. For b), don't forget that each experimental condition is repeated 5 times.

Denis and Claude
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