Réponse:
[tex]\binom{3}{7} + \binom{5}{21} = \binom{3 \times 3}{7 \times 3} + \binom{5}{21} = \binom{9}{21} + \binom{5}{21} = \binom{14}{21}[/tex]
[tex]\binom{15}{8} - \binom{5}{4} = \binom{15}{8} - \binom{5 \times 2}{4 \times 2} = \binom{15}{8} - \binom{10}{8} = \binom{5}{8} [/tex]
[tex]\binom{23}{100} - \binom{3}{20} = \binom{23}{100} - \binom{3 \times 5}{20 \times 5} = \binom{23}{100} - \binom{15}{100} = \binom{8}{100} = \binom{4}{50} = \binom{2}{25} [/tex]
[tex] \binom{23}{44} - \binom{5}{11} = \binom{23}{44} - \binom{5 \times 4}{11 \times 4} = \binom{23}{44} - \binom{20}{44} = \binom{3}{44} [/tex]
[tex] \binom{1}{1} - \binom{7}{4} = \binom{1 \times 4}{1 \times 4} - \binom{7}{4} = \binom{4}{4} - \binom{7}{4} = - \binom{3}{4} [/tex]
