以下是一个解决这个问题的Python代码：

def count_happy_days(candies):
    combinations = set()
    happy_days = 0

    for i in range(len(candies)-1):
        for j in range(i+1, len(candies)):
            combination = (candies[i], candies[j])
            if combination not in combinations:
                combinations.add(combination)
                happy_days += 1

    return happy_days

candies = [1, 1, 4, 5, 1, 4]
result = count_happy_days(candies)
print(result)

运行这段代码，输出结果为3，表示小美最多有3天会很高兴。