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Sagot :
Answer:
a) Number of ways to choose 4 colors from 17 if the order matters =57120
b) Number of ways to choose 4 colors from 17 if the order does not matter = 2380
Explanation:Total number of colors, n = 17
Number of colors to choose, k = 4
a) Number of ways to choose 4 colors from 17 if the order matters = 17P4
[tex]\begin{gathered} nPk=\frac{n!}{(n-k)!k!} \\ \\ 17P4=\frac{17!}{(17-4)} \\ \\ 17P4=\frac{17!}{13!4!} \\ \\ 17P4=\frac{17\times16\times15\times14\times13!}{13!} \\ \\ 17P4=17\times16\times15\times14 \\ \\ 17P4=57120 \end{gathered}[/tex]b) Number of ways to choose 4 colors from 17 if the order does not matter = 17C4
[tex]\begin{gathered} nCk=\frac{n!}{(n-k)!k!} \\ \\ 17C4=\frac{17!}{(17-4)!4!} \\ \\ 17C4=\frac{17!}{13!4!} \\ \\ 17C4=\frac{17\times16\times15\times14\times13!}{13!\times4\times3\times2\times1} \\ \\ 17C4=2380 \end{gathered}[/tex]
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