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Ya as one can go with 5 ways except itself means one video game can combine with 5 different other video games as it can not combine with itself ...and there can be only 3 pairs to be available in the 6 video games so 5*3=15 answer is 15

We start naming your video games, there are 6 , right? Let them be named as {A,B,C,D,E,F}.
Now, choose any one of the six, say you chose A, now this element can combine with five other in this manner, AB,AC,AD,AE,AF. But each of these pairs are taken twice, for example if you've chosen B it can form pairs BA,BC,BD,BE,BF. You can observe that there are two of each pairs of A,B namely AB & BA. Hence the the total number of pairs formed is going to slash to half. Total number of pairs are 6(5)/2 = 15