Three molecules of type A, three of type B, three of type C, and three of type D are to be linked together to form a chain molecule. One such chain molecule is ABCDABCDABCD,and another is BCDDAAABDBCC. a. How many such chain molecules are there? [ Hint: If the three A's were distinguishable from one another- A1 A2, A3-and the Bs, Cs, and Vs were also, how many molecules would there be? How is this number reduced when the subscripts are removed from the A's?] b. Suppose a chain molecule of the type described is randomly ·what is the probability that all three molecules of each type end up next to one another (such as in BBBAAADDDCCC)?

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 1EQ: 1. Suppose that, in Example 2.27, 400 units of food A, 600 units of B, and 600 units of C are placed...
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Three molecules of type A, three of type B, three of type C, and three of type D are to be linked together to form a chain molecule. One such chain molecule is ABCDABCDABCD,and another is BCDDAAABDBCC.

a. How many such chain molecules are there? [ Hint: If the three A's were distinguishable from one another- A1 A2, A3-and the Bs, Cs, and Vs were also, how many molecules would there be? How is this number reduced when the subscripts are removed from the A's?]

b. Suppose a chain molecule of the type described is randomly ·what is the probability that all three molecules of each type end up next to one another (such as in BBBAAADDDCCC)?

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