Bob, Carol, Ted, and Alice are splitting 25 identical jelly beans. Bob wants at least one jelly bean, Carol wants at least two jelly beans, Ted wants at least three jelly beans, and Alice wants at least four jelly beans. How many ways are there to distribute the jelly beans?

It is widely assumed that people need to engage in intellectual activities such as solving crossword puzzles or mathematics problems in order to maintain mental sharpness as they age. in fact, however, simply talking to other people—that is, participating in social interaction, which engages many mental and perceptual skills—suffices. evidence to this effect comes from a study showing that the more social contact people report, the better their mental skills. which of the following, if true, most seriously weakens the force of the evidence cited? (a) as people grow older, they are often advised to keep exercising their physical and mental capacities in order to maintain or improve them. (b) many medical conditions and treatments that adversely affect a person's mental sharpness also tend to increase that person's social isolation. (c) many people are proficient both in social interactions and in solving mathematical problems. (d) the study did not itself collect data but analyzed data bearing on the issue from prior studies. (e) the tasks evaluating mental sharpness for which data were compiled by the study were more akin to mathematics problems than to conversation.