Question Number 103406 by mr W last updated on 16/Jul/20

100 students are standing in a row.  4 students should be selected in the  way that no two of them are next to  each other. how many ways do you  have to do this?

Commented bybobhans last updated on 15/Jul/20

n(S) = C_4 ^(100)  = ((100!)/(4!.96!))  n(A) = 100!−50.C_2 ^(50)  = 100!−50×((50!)/(2!.48!))  p(A) = ((100!−50.((50!)/(2.48!)))/(100!)) × 4!.96!  =((100!−((50.50!)/(2.48!)))/(100.99.98.97)) × 4! = ((100!−((50.50.49)/2))/(100.99.98.97)) ×4!

Commented bymr W last updated on 16/Jul/20

3 464 840 ways

Commented bymr W last updated on 16/Jul/20

answer see Q103716