Jessica runs a small landscaping business. (Please provide explanation)

Question

1.Jessica runs a small landscaping business. She has on hand 12 rose bushes, 16 small

shrubs, 11 types of evergreen seedlings, and 18 kinds of lilies. In how many ways can

Jessica fill an order if a customer wants:

Please help I don't understand, explain if you can!

a) 15 varieties consisting of 4 roses, 3 shrubs, 2 evergreens, and 6 lilies? The answer says its 2.830267 x 10^11, Please show how.

b) Either 4 different roses or 6 different lilies?

Also how would you know when to use the two formulas in questions like these? (n r) <- supposed to be flipped vertically. And nCr = n! / (n - r)!r!

Answer 1

The answer to the first question is the product of 4 binomial coefficients (which I will not calculate for you);

₁₂C₄ * ₁₆C₃ * ₁₁C₂ * ₁₈C₆ but I have little doubt that the answer can be as big as you quote.

For the 2nd question you need to remember that

P(A or B) = P(A) + P(B) - P(A and B).

I am not sure how to answer you own question which is not clear. If you can re=phrase and clarify in a comment, I will try to respond.