Question 19188: In how many ways can Abby, Bonnie, Chuck, Dennis, Ed and Fred line up at the water fountain so that the two girls are not beside each other? ____________ ways
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! In how many ways can Abby, Bonnie, Chuck, Dennis, Ed and Fred line up at the water fountain so that the two girls are not beside each other? ____________ ways ..
there are 2 girls and 4 boys...it is assumed that the question is for standing in a steraight line at the water fountain and not standing in a circle around the fountain
in such a case let the 4 boys be made to stand first as say
xxxxB1xxxxxB2xxxxxB3xxxxxB4xxxxx.........where B1,B2,B3 and B4 stand for 4 boys.now since the girls should not be together ,we can put them in the gaps between the boys OR on outer side of the last positioned boys..shown by xxxxx
in the figure
so now 4 boys can be arranged in 4*3*2*1=24 ways.
2 girls can be arranged in 3+2=5 positions in 5*4=20 ways.
so we have in all 24*20 =480 arrangements possible.
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