Question

某次数学测验中，学号i(i=1，2，3，4)的四位同学的考试成绩f(i)∈{90，92，93，96，98}，若满足f(1)<f(2)

某次数学测验中，学号i(i=1，2，3，4)的四位同学的考试成绩f(i)∈{90，92，93，96，98}，若满足f(1)<f(2)≤f(3)<f(4)，则这四位同学的考试成绩的所有可能情况的种数为?
求过程

Answer 1

解：①若f(1)<f(2)<f(3)<f(4)，则C5-4=5，列举法验证：{90,92,93,96}，{90,92,93,98}，{90,92,96,98}，{90,93,96,98}，{92,93,96,98}
②若f(1)<f(2)=f(3)<f(4)，则C5-3=10，列举法验证：{90,92,92,93}，{90,92,92,96}，{90,92,92,98}，{90,93,93,96}，{90,93,93,98}，{90,96,96,98}，{92,93,93,96}，{92,93,93,98}，{92,96,96,98}，{93,96,96,98}
③故总数为C5-4+C5-3=5+10=15

Answer 2

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Answer 3

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