Amit has five friends: 3 girls and 2 boys. Amit’s wife also has 5 friends: 3 boys and 2 girls. In how many maximum numbers of different ways can they invite 2 boys and 2 girls such that two of them are Amit’s friends and two are his wife’s?

To find the total number of ways, we must consider all possible combinations where Amit invites 2 friends and his wife invites 2 friends, resulting in a total group of 2 boys and 2 girls. Amit has 3 girls (G) and 2 boys (B). His wife has 3 boys (b) and 2 girls (g). There are three possible scenarios to satisfy the requirement: Scenario 1: Amit invites 2 boys and his wife invites 2 girls. Amit chooses 2 boys from 2: 1 way. Wife chooses 2 girls from 2: 1 way. Total: 1 times 1 = 1 way. Scenario 2: Amit invites 2 girls and his wife invites 2 boys. Amit chooses 2 girls from 3: 3 ways. Wife chooses 2 boys from 3: 3 ways. Total: 3 times 3 = 9 ways. Scenario 3: Amit invites 1 boy and 1 girl, and his wife invites 1 boy and 1 girl. Amit chooses 1 boy from 2 and 1 girl from 3: 2 times 3 = 6 ways. Wife chooses 1 boy from 3 and 1 girl from 2: 3 times 2 = 6 ways. Total: 6 times 6 = 36 ways. Adding the ways from all scenarios: 1 + 9 + 36 = 46. Therefore, the maximum number of different ways is 46. Correct option is C.