Решебник по алгебре и начала математического анализа 10 класс Алимов Задание 1080

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\[1)\ C_{7}^{1} = \frac{7!}{(7 - 1)! \bullet 1!} = \frac{7!}{6!} =\]

\[= \frac{7 \bullet 6!}{6!} = 7;\]

\[2)\ C_{6}^{1} = \frac{6!}{(6 - 1)! \bullet 1!} = \frac{6!}{5!} =\]

\[= \frac{6 \bullet 5!}{5!} = 6;\]

\[3)\ C_{8}^{2} = \frac{8!}{(8 - 2)! \bullet 2!} = \frac{8!}{6! \bullet 2} =\]

\[= \frac{8 \bullet 7 \bullet 6!}{6! \bullet 2} = 4 \bullet 7 = 28;\]

\[4)\ C_{7}^{2} = \frac{7!}{(7 - 2)! \bullet 2!} = \frac{7!}{5! \bullet 2} =\]

\[= \frac{7 \bullet 6 \bullet 5!}{5! \bullet 2} = 7 \bullet 3 = 21;\]

\[5)\ C_{7}^{3} = \frac{7!}{(7 - 3)! \bullet 3!} = \frac{7!}{4! \bullet 3 \bullet 2} =\]

\[= \frac{7 \bullet 6 \bullet 5 \bullet 4!}{4! \bullet 6} = 7 \bullet 5 = 35;\]

\[6)\ C_{8}^{3} = \frac{8!}{(8 - 3)! \bullet 3!} = \frac{8!}{5! \bullet 3 \bullet 2} =\]

\[= \frac{8 \bullet 7 \bullet 6 \bullet 5!}{5! \bullet 6} = 8 \bullet 7 = 56;\]

\[7)\ C_{9}^{8} = \frac{9!}{(9 - 8)! \bullet 8!} = \frac{9!}{1! \bullet 8!} =\]

\[= \frac{9 \bullet 8!}{8!} = 9;\]

\[8)\ C_{10}^{9} = \frac{10!}{(10 - 9)! \bullet 9!} = \frac{10!}{1! \bullet 9!} =\]

\[= \frac{10 \bullet 9!}{9!} = 10;\]

\[9)\ C_{15}^{15} = \frac{15!}{(15 - 15)! \bullet 15!} =\]

\[= \frac{15!}{0! \bullet 15!} = \frac{1}{1} = 1;\]

\[10)\ C_{12}^{12} = \frac{12!}{(12 - 12)! \bullet 12!} =\]

\[= \frac{12!}{0! \bullet 12!} = \frac{1}{1} = 1;\]

\[11)\ C_{30}^{0} = \frac{30!}{(30 - 0)! \bullet 0!} =\]

\[= \frac{30!}{30! \bullet 1} = \frac{1}{1} = 1;\]

\[12)\ C_{40}^{0} = \frac{40!}{(40 - 0)! \bullet 0!} =\]

\[= \frac{40!}{40! \bullet 1} = \frac{1}{1} = 1;\]

\[13)\ C_{50}^{48} = \frac{50!}{(50 - 48)! \bullet 48!} =\]

\[= \frac{50!}{2! \bullet 48!} = \frac{50 \bullet 49 \bullet 48!}{2 \bullet 48!} =\]

\[= 25 \bullet 49 = 1225;\]

\[14)\ C_{40}^{38} = \frac{40!}{(40 - 38)! \bullet 38!} =\]

\[= \frac{40!}{2! \bullet 38!} = \frac{40 \bullet 39 \bullet 38!}{2 \bullet 38!} =\]

\[= 20 \bullet 39 = 780;\]

\[15)\ C_{70}^{2} = \frac{70!}{(70 - 2)! \bullet 2!} =\]

\[= \frac{70!}{68! \bullet 2} = \frac{70 \bullet 69 \bullet 68!}{68! \bullet 2} =\]

\[= 35 \bullet 69 = 2415;\]

\[16)\ C_{60}^{2} = \frac{60!}{(60 - 2)! \bullet 2!} =\]

\[= \frac{60!}{58! \bullet 2!} = \frac{60 \bullet 59 \bullet 58!}{58! \bullet 2} =\]

\[= 30 \bullet 59 = 1770.\]