Mr. Money
There are in the Netherlands at the moment 4 coins less than Euro 1 in vogue, namely 50 cent coins, 20 cent coins, 10 cent coins and 5 cent coins. Mr Money has a bucket full of these 4 kinds of coins. He grasps at random 4 coins out of the well mixed bucket. The probability that he has a total value of 80 cents is , where and are coprime positive integers. What is ?
The answer is 38.
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1 solution
Let in a grasp x(1) = number of 50 cent coins, x(2) = number of 20 cent coins, x(3) = number of 10 cent coins and x(4) = number of 5 cent coins. How many solutions (x(1), x(2), x(3), x(4)) does the equation * x(1) + x(2) + x(3) + x(4) = 4 * have, where 0 <= x(i) <= 4 are integers? The number of solutions is equal to the number of ways the four objects x(1), x(2), x(3) and x(4) can be divided by 3 "+"signs. In other words to point out 3 objects ( the "+"signs) among 7 objects.Thus (7!)/(3! x 4!) = 35 ways. Each of the solutions (0, 4, 0, 0), (1, 0, 3, 0) and (1, 1, 0, 2) gives a total of 80 cents. Thus a/b = 3/35 and a + b = 38