6; 6. 1; 6,2: 6. three; 6,4; 6. five: 6,6. The previous counting rule is prolonged effectively to figure out the variety of methods greater than issues can take place jointly. If something can ensue in somebody of ok, methods, a moment factor in someone of k2 methods, a 3rd factor in any of k3 methods, etc, via an nth factor in someone of ok" methods, then the variety of methods for all n issues to take place jointly is (k, ) (k2 ) (k3 ) ... (k" ). hence, if 3 cash are tossed, every one toss leading to one in all attainable results, then there's a overall of attainable results for the 3 tosses jointly: H,H,H; H,H,T: H,T. H; H. T. T: T,H. H, T,H,T; T,T,H; T. T,T. equally. if 3 cube are thrown. there are (k, )( k2)( k3) = (6) (6)( 6) = sixty three = 216 attainable results: if cube and 3 cash are thrown, there are *What we realize as steel cash originated presently after 650 B. c. E. -perhaps in historic Lydia (located at the Aegean Sea in what's now western Turkey). From the start, the obverse and opposite facets of cash have had assorted designs. in earliest instances with the obverse in most cases depicting animals and, later, deities and rulers (Sutherland. 1992). cube have lengthy been used for either video games and faith. They date from approximately 3000 years S. C. E. , with the trendy traditional association of dots at the six faces of a cubic die (I contrary 6, 2 contrary five, and three contrary four) turning into dominant round the heart of the fourteenth century B. C. E. (David, 1962: 10). in fact. the association of the numbers I via 6 at the six faces has no impression at the end result of throwing a die. part five. 2 diversifications fifty one (kd(k2)(k3)(k4)(ks) = (6)(6)(2)(2)(2) = (62 )(23) = 288 results; etc. instance five. 1 supplies organic examples of counting attainable results. instance five. 1 Counting attainable results (a) A linear association of 3 deoxyribonucleic acid (DNA) nucleotides is named a triplet. A nucleotide could comprise a person of 4 attainable bases: adenine (A), cytosine (C), guanine (G), and thymine (T). what number various triplets are attainable? because the first nucleotide within the triplet can be somebody of the 4 bases (A; C; G; T), the second one could be a person of the 4. and the 3rd will be someone of the 4. there's a overall of (k d (k2)( k3) = (4)( four )( four) = sixty four attainable results: that's, there are sixty four attainable triplets: A. A. A; A. A, C; A. A, G; A. C, A; A. C. C; A, C, G; A, G. A; A. G. C; A, G. G; etc. A. A. T; A. C, T; A. G. T; (b) If a diploid cellphone includes 3 pairs of chromosomes. and one member of every pair is located in every one gamete, what percentage varied gametes are attainable? because the first chromosome may perhaps ensue in a gamete in a single of 2 varieties, as may well the second one and the 3rd chromosomes. allow us to designate one of many pairs of chromosomes as "long," with the individuals of the pair being L, and L2; one pair as "short. " indicated as S, and S2; and one pair as "midsized," categorised M, and M2. Then the 8 attainable results could be represented as L,. M,. S,: L2. M"S,: five. 2 L,. M"S2: L2,M"S2: L"M2,S,: L2. M2,S,: L"M2,S2: L2, M2.