问题 填空题

已知集合A={1,2,3},B={5,6,7,8},映射f:A→B满足f(3)≥f(1)≥f(2),则这样的映射f共有______个?

答案

记f(3),f(1),f(2)对应的函数值分别为(a,b,c),

则满足条件情况共有:

(8,8,8),(8,8,7),(8,8,6),(8,8,5),(8,7,7),

(8,7,6),(8,7,5),(8,6,6),(8,6,5),(8,5,5),

(7,7,7),(7,7,6),(7,7,5),(7,6,6),(7,6,5)

(7,5,5),(6,6,6),(6,6,5),(6,5,5),(5,5,5)共20种

故答案为:20.

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