Fighting Game Face-Offs

Probability Level 2

Sarah is a video game designer currently working on a fighting game. She'd like to have an animated and voiced "face-off" between the fighters before each match starts. This interaction will be unique for every possible 1v1 match-up among the game's 10 characters. How many of these interactions will she have to design?

Note : In this fighting game, it is possible for a character to be matched up against the same character. The order of the fighters does not matter (if the order is switched, the animation is simply mirrored, and this does not count as an additional animation).

20 55 60 90

2 solutions

Jerry McKenzie
Jan 14, 2018

Easily 2 cases:

If they choose the same character, there are only $10$ pairs, one for each character.

If they choose different characters, then the interaction is the same for each pair chosen, without order. As follows:

$\binom{10}{2}=\frac{10!}{2!\cdot 8!}=\frac{10\cdot 9\cdot 8!}{2\cdot 8!}=5\cdot 9=45$

Therefore, the total amount of pairs are $10+45=55$

Ankur Gupta
Dec 28, 2017

We already given that , In this fighting game, it is possible for a character to be matched up against the same character. So every person matches with another person. Total characters-10 1 character fight with another 9 characters. So , it will be same for other characters. 2 nd character fight with 8 characters....... ............ Etc.. 10+9+8+7+6+5+4+3+2+1=55.

Fighting Game Face-Offs

2 solutions

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