21>2 CrUieiatii of Hjipothesin of Lliilagc (uid Crossing Over 



K our crossings : (r -- 1) ^^-j^,^^^^ ^ + ^ Vx2x3 <"-'■>• 



„. . , ,An-r) ... hi-r-Z) 



Five crossings: (»• - 1) ' .„ — ; ^ 



Ix2xdx4 



(r-l)(r-2)(,--3 ) (k-|-) (« -r -1) (r- l)(r - 2) (r - 3)(f - 4) (r- 5 ) 

 1x2x3 1x2 1x2x3x4x5 



The following formulae give the numbers of C. O.'s + N. C. O.'s. 



One crossing : n-1. 



^ (ji-l)(n-2) 



Two crossings : ,— - 



1x2 



("- 1) ("-2)(n-3) 



Three crossings: ^ V ,. - t ■ Etc. 



1x2x3 



Noil- Cross-Overs. 



AB AC AD .IE AF .1(1 AH AI AJ AK AL AM AN AO Al> .i(J AK AS AT AU AV AW AX AY AZ 



1 2 3 4 5 (i 7 8 9 10 11 12 13 U 15 16 17 18 19 20 21 22 23 24 



23 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 



22 22 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 



21 21 21 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 



20 20 20 20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 



19 19 19 19 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 



18 18 18 18 18 18 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 



17 17 17 17 17 17 17 1 2 3 4 5 6 7 8 9 10 11 12 13 11 15 16 17 



16 16 16 16 16 16 16 16 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 



15 15 15 15 15 15 15 15 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 



14 14 14 14 14 14 14 14 14 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 



13 13 13 13 13 13 13 13 13 13 13 1 2 3 4 5 6 7 8 9 10 11 12 13 



12 12 12 12 12 12 12 12 12 12 12 12 1 2 3 4 5 6 7 8 9 10 11 12 



11 11 11 11 11 11 11 11 11 U 11 11 11 1 2 3 4 5 6 7 8 9 10 11 



10 10 10 10 10 10 10 10 10 10 10 10 10 10 1 2 3 4 5 6 7 8 9 10 



99999999999999 9 012 3456789 



88888888888 8 8888012 345678 



77777777777777777012 34567 



66666 6 6666666666660123456 



55555555555 5 5555555012 345 



4444444444444444444401234 



33333333333333 3 333333012 3 



2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 12 



111111111111111111111110 1 



