Atalentcontesthas8contestants.Judgesmustawardprizesforfirst,second,andthirdpalces,withnoties.(a)Inhowmanydifferentwayscanthejudgesawardthe3prizes?(b)Howmanydifferentgroupsof3peoplecangetprizes?a的答案为336b56

Question

A talent contest has 8 contestants.Judges must award prizes for first,second,and third palces,with no ties.
(a) In how many different ways can the judges award the 3 prizes?
(b)How many different groups of 3 people can get prizes?
a 的答案为336 b56 排列组合都忘了

Answer 1

（1）第1,2,3位置.第1位置从8人取1,第2位置,从剩下7人取1,第3位置,从剩下6人取1, 结果=8*7*6=336
（2）8个人中有3个人有机会获奖,C（3,8）=8*7*6/（3*2*1）=56