Page:Astounding Science Fiction v54n06 (1955-02).djvu/133

, we don't have to do that. The number of combinations can be calculated indirectly from the data we already have.

Thus, if we have n different objects, then the number of ways in. which they can be arranged in a line is equal to the product of all the integers from n down to 1. The number of combinations of four objects, for instance, is: 4 x 3 x 2 x 1, or 24. This is the number we found by actually writing out all the different combinations (see Figure 5). The product of all the integers from n to 1 is called "factorial n" and is symbolized as n!

If the n objects are not all different, an additional complication is introduced. Suppose that our very small four-amino-acid protein is made up of two amino acids of one kind and two of another. Let's symbolize the amino acids as a, a*, b and b*. The twenty-four theoretical combinations are presented in Figure 7a. But if a and a* are indistinguishable, and b and b* likewise, then the combination ab* is identical, for all practical purposes, with a*b, a*b*, and ab. The combination aba*b* is identical with a*bab*, ab*a*b and so on. The total number of different combinations among those RV 134