Jimmi and Vishal are planning a dinner party. Vishal has 4 vegetarian friends and 3 non-vegetarian friends, while Jimmi has 3 vegetarian friends and 4 non-vegetarian friends. They decide to invite 4 friends in total and it was decided that both of them will invite two of their friends and also ensure that there are a total of 2 vegetarians and 2 non-vegetarians friends. How many ways can they invite their friends to the dinner party?

To solve this problem, we need to consider the different combinations of friends that Jimmi and Vishal can invite.

1. First, let's consider the vegetarian friends. Vishal has 4 vegetarian friends and he can invite 2 of them. The number of ways he can do this is given by the combination formula C(n, r) = n! / [(n-r)!r!], where n is the total number of items, and r is the number of items to choose. So, C(4, 2) = 4! / [(4-2)!2!] = 6 ways.

   Similarly, Jimmi has 3 vegetarian friends and he can invite 0 of them (since Vishal is already inviting 2 vegetarian friends). So, C(3, 0) = 3! / [(3-0)!0!] = 1 way.

   Therefore, the total number of ways to invite the vegetarian friends is 6 * 1 = 6 ways.

2. Next, let's consider the non-vegetarian friends. Vishal has 3 non-vegetarian friends and he can invite 0 of them (since he is already inviting 2 vegetarian friends). So, C(3, 0) = 3! / [(3-0)!0!] = 1 way.

   Similarly, Jimmi has 4 non-vegetarian friends and he can invite 2 of them. So, C(4, 2) = 4! / [(4-2)!2!] = 6 ways.

   Therefore, the total number of ways to invite the non-vegetarian friends is 1 * 6 = 6 ways.

3. Finally, to find the total number of ways to invite all the friends, we multiply the number of ways to invite the vegetarian friends by the number of ways to invite the non-vegetarian friends. So, 6 * 6 = 36 ways.

Therefore, Jimmi and Vishal can invite their friends to the dinner party in 36 different ways.