某篮球队有12名队员,有6名打前锋位,4名打后卫位,甲.乙两名既能打前锋又能打后卫位(出场阵容为3名前锋,2名后卫),共有多少种出场阵容?最好算出来啊····谢谢·····_百度作业帮
某篮球队有12名队员,有6名打前锋位,4名打后卫位,甲.乙两名既能打前锋又能打后卫位(出场阵容为3名前锋,2名后卫),共有多少种出场阵容?最好算出来啊····谢谢·····
某篮球队有12名队员,有6名打前锋位,4名打后卫位,甲.乙两名既能打前锋又能打后卫位(出场阵容为3名前锋,2名后卫),共有多少种出场阵容?最好算出来啊····谢谢·····
答:1:首先,剔除甲乙2个多面手考虑,从6个前锋选3个 C(3,6),从4个后卫选2个 C(2,4),共C(3,6)*C(2,4)种情况;2:加入甲乙中任一个为前锋,即C(1,2),从6个前锋中选2个前锋 C(2,6),从4个后卫中选2个后卫 C(2,4),共C(2,6)* C(2,4)*C(1,2)种情况;3:同理,从甲乙中任选一个为后卫,共C(3,6)*C(1,4)*C(1,2)种情况;4:再把甲乙都加入同时为前锋C(1,6)*C(2,4),同时为后卫C(3,6),一前锋一后卫C(2,6)*C(1,4)*C(1,2).把上面的四种情况加起来得:636种 ························································································································································································································································(我是曾经的4楼.)补充一下,我是刚逛的时候又看到这道题的,然后看到了5楼的回答.我想甲乙在不同位置阵容应该是不同的,毕竟选手所处位置已经不同.希望lz知道正确答案后公布一下.
1:从六个前锋选三个前锋 C(3,6),从四个后卫选两个后卫 C(2,4),这种情况数C(3,6)*C(2,4)2:从六个前锋加甲乙中选三个前锋 C(3,8),从四个后卫中选两个后卫 C(2,4),这种情况数C(3,8)* C(2,4)3:从六个前锋加甲或乙选三个前锋 2C(3,7),从四个后卫加甲或乙中选两个后卫2C(2,5),这种情况数2C(3,7)* 2C(2,5)