Cosplay Lineup 2!
Probability
Level
2
Of a group of six cosplayers, two are dressed as the same character.
How many ways can the group line up (in a row) for a photo so that the two identical characters stand next to each other?
The answer is 240.
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1 solution
given that, the two cos-players stand next to each other, so name the players as "a and b" when a and b are in 1st and 2nd position then the other four players can be arranged in 4x3x2x1=24. similarly, when a and b are in 2nd and 3rd position then again no.of arrangements=24, then 3rd and 4th.... 24, next when in 4th and 5th position....24, at last when in 5th and 6th position...24.. no. of ways=24+24+24+24+24=24(5)=120. in the above cases the player a was in front of b .thus when b is in front of a the no. of possible ways of arrangements=24(5)=120 thus total no. of ways "240"