问题
选择题
若3n个学生排成一排的排法种数为a,这3n个学生排成三排,每排n人的排法种数为b,则( )
A.a>b
B.a<b
C.a=b
D.a,b的大小由n确定
答案
3n个学生排成一排的排法有a=
=(3n)!A 3n3n
3n个学生排成三排,每排n人的排法种数为b=
•A n3n
•A n2n
=A nn
•(3n)! (2n)!
•n!=(3n)!=a(2n)! n!
故选C
若3n个学生排成一排的排法种数为a,这3n个学生排成三排,每排n人的排法种数为b,则( )
A.a>b
B.a<b
C.a=b
D.a,b的大小由n确定
3n个学生排成一排的排法有a=
=(3n)!A 3n3n
3n个学生排成三排,每排n人的排法种数为b=
•A n3n
•A n2n
=A nn
•(3n)! (2n)!
•n!=(3n)!=a(2n)! n!
故选C