nately, we don't have to do that. The number of combinations can be calculated indirectly from the data we already have.
a-b-c-d-e-f-g-h-i-j-k-l-m-n-o-p-q-r-s-t-a-b-c-d-e-f-g-h-i-j-k-l-m-n-o-p-q-r-s-a-b-c-d-e-f-g-h-i-j-k-l-m-n-o-p-q-r-s-a-b-c-d-e-f-g-h-i-j-k-l-m-n-o-p-q-r-a-b-c-d-e-f-g-h-i-j-k-l-m-n-o-p-q-a-b-c-d-e-f-g-h-i-j-k-l-m-n-o-p-a-b-c-d-e-f-g-h-i-j-k-l-m-n-o-p-a-b-c-d-e-f-g-h-i-j-k-l-m-n-o-p-a-b-c-d-e-f-g-h-i-j-k-l-m-n-o-p-a-b-c-d-e-f-g-h-i-j-k-l-m-n-o-p-a-b-c-d-e-f-g-h-i-j-k-l-m-n-o-p-a-b-c-d-e-f-g-h-i-j-k-l-m-n-o-a-b-c-d-e-f-g-h-i-j-k-l-m-n-o-a-b-c-d-e-f-g-h-i-j-k-l-m-n-o-a-b-c-d-e-f-g-h-i-j-k-l-m-n-a-b-c-d-e-f-g-h-i-j-k-l-m-n-a-b-c-d-e-f-g-h-i-j-k-l-m-n-a-b-c-d-e-f-g-h-i-j-k-l-m-n-a-b-c-d-e-f-g-h-i-j-k-l-a-b-c-d-e-f-g-h-i-j-k-l-a-b-c-d-e-f-g-h-i-j-k-a-b-c-d-e-f-g-h-i-j-k-a-b-c-d-e-f-g-h-i-j-a-b-c-d-e-f-g-h-i-j-a-b-c-d-e-f-g-h-i-a-b-c-d-e-f-g-h-i-a-b-c-d-e-f-g-h-i-a-b-c-d-e-f-g-h-i-a-b-c-d-e-f-g-h-i-a-b-c-d-e-f-g-h-i-a-b-c-d-e-f-g-h-a-b-c-d-e-f-g-h-a-b-c-d-e-f-g-h-a-b-c-d-e-f-g-a-b-c-d-e-f-g-a-b-c-d-e-f-a-b-c-d-e-a-b-c-d-e-a-b-c-d-a-b-c-d-a-b-c-d-a-b-c-d-a-b-c-d-a-b-c-d-a-b-c-d-a-b-c-d-a-b-c-d-a-b-c-d-a-b-c-a-b-c-a-b-a-b-a-b-a-b-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a
Figure 6. One possible arrangement of the amino acids in the hemoglobin molecule.
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!
Figure 7a. The total arrangements of four amino acids, two of one kind and two of another. |
a-a-b-b a-b-a-b a-b-b-a b-a-a-b b-a-b-a b-b-a-a Figure 7b. The different arrangements of four amino acids, two of one kind and two of another. |
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
134
Astounding Science-Fiction
