A gardener plans to plant nine rose bushes. Two are red, three are white, and fo

Question

A gardener plans to plant nine rose bushes. Two are red, three are white, and four yellow. How many distinguishable arrangements can be made if she plants then in a straight line? FOR CREDIT At a family restaurant, the menu has 8 entrees, 12 vegetables, 4 drinks, and 9 desserts. For a cost of $6.59, you get to choose 1 entree, 3 vegetables, 1 drink, and 2 desserts. How many different plates can be made? FOR CREDIT My ATM card code is made of four single digits (e.g. 3829, this isn't it, so don't even think about it). You can repeat the digits (for example, 8888 is a valid code). The ATM machine is programmed to take the card if three unsuccessful attempts are made. If you try to guess my code, what is the probability that the ATM machine will take the card (i.e. you fail all three time Suppose that you are a somewhat intelligent thief and do not reuse a code that you have attempted. FOR CREDIT. The work must be correct too.

Explanation / Answer

20) No of arrangements possible = 9!/(2!x4!x3!)

= 1260

21) No of plates possible = 8x12C3x4x9C2 = 253440

(nCr = n!/(r!x(n-r)!)

22) Total number of codes possible = 104 = 10000

Number of possible attempts is 3

P(ATM machine will take the card) = 3/10000 = 0.0003

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