1. Formulae for predicting number of crosses from all‑combination data.

The following formulae have been found to be useful in dealing with yield data of all‑combination field trials. Letting "n" represent the initial number of inbreds, the well‑known formula 1/2n (n‑1) predicts the total nunber of single crosses, while 1/2n (n‑1) (n‑2) shows the number of three‑way crosses which can be predicted from the single cross yields, and 1/8n (n‑1) (n‑2) (n‑3) gives the number of double crosses which can be predicted from the same single cross yields. The following table shows the relationships obtained by use of these formulae with various numbers of inbreds used initially in making up the all‑combination single crosses. In every case all reciprocal combinations are excluded.

 Number of inbreds Possible number of crosses of two inbreds Possible number of crosses of three inbreds Possible number of crosses of four inbreds 1 0 0 0 2 1 0 0 3 3 3 0 4 6 12 3 5 10 30 15 6 15 60 45 7 21 105 105 8 28 168 210 9 36 252 378 10 45 360 630