Question 15
Warren has 39 coins, 2 are gold coins and the other 37 are silver coins. Warren puts these coins in a line. Then Warren chooses the coins that satisfy one of the following conditions:
(i) choose two silver coins so that there is exactly one gold coin between them;
(ii) choose one gold coin and one silver coin so that the other gold coin does not lie between them;
(iii) just choose exactly one gold coin.
With the different positions of the two gold coins, the number of Warren’s ways to choose are also different. What is the maximum number of Warren’s different choosing ways? Detailed solutions are needed.
(i) choose two silver coins so that there is exactly one gold coin between them;
(ii) choose one gold coin and one silver coin so that the other gold coin does not lie between them;
(iii) just choose exactly one gold coin.
With the different positions of the two gold coins, the number of Warren’s ways to choose are also different. What is the maximum number of Warren’s different choosing ways? Detailed solutions are needed.