Answer: The answer is 9.
Step-by-step explanation: Given that five members of gymnastics team and 7 members of weight lifting team are travelling in two vans to the rival school for competition. We are to find the number of ways in which they can ride in two vans such that no van contains more than eight passengers and there is at least one member of each team in each van.
Let 'g' and 'w' denote a member of gymnastics team and weight lifting team respectively.
Then, the possibilities are
For 1 g, we can choose 3w, 4w, 5w, 6w.
For 2g, we can choose 2w, 3w, 4w, 5w, 6w.
For 3g, we can choose 1w, 2w, 3w, 4w, 5w.
For 4g, we can choose, 1w, 2w, 3w, 4w.
Therefore, there are (4 + 5 + 5 + 4) = 18 ways.
Since, here the position of the vans does not matter, so the options are double here. Hence, we must divide it by 2.
Thus, the total number of ways = 9.
