Consider a world consisting of three stocks, A$,$ B$,$ and C$.$ Each stock has $100$ shares outstanding. The world consists of $10$ investors. Investor #$1$ is a passive indexer who holds $50\%$ of the market. Evaluate the following statements, are they true or false, and $($one sentence$)$ why?

a$)$ Investor #$1$ holds $50$ shares each in A$,$ B$,$ C $($no matter what the prices are$).$

b$)$ Investors #$2-$ #$10,$ as a group, hold $50$ shares each in A$,$ B$,$ C $($no matter what the prices are$).$

c$)$ It is possible that some of investors #$2-$ #$10$ will have returns that are higher than market returns.

d$)$ It is possible that all of investors #$2-$ #$10$ will have returns that are higher than market returns.

e$)$ If investor #$2$ holds $3$ shares of stock A but nothing else, it is obvious that he is a fool. There is no conceivable rational reason for him to do this.

f$)$ If investor #$2$ holds $3$ shares of stock A but nothing else, then it is mathematically impossible that investors #$3-$ #$10$ as a group are just holding stocks in proportion to their market capitalization. It is mathematically impossible for everyone except investor #$2$ to $$just hold the market$$ or $$just hold index funds$.$