206. Characteristics of men. In a certain group of men, $70 \%$ have brown eyes; $70 \%$ have dark hair, $85 \%$ are taller than 5 feet 8 inches, and $90 \%$ weigh more than 140 pounds. What percentage of men definitely have all four of these characteristics?
206. Let's take 100 men and record each of the four characteristics for each man who possesses the characteristic. As a result, we will have $70+75+85+90=320$ records. Since there are 320 records for 100 men, we can observe that with the most even distribution of characteristics among the men, each man would have at least 3 characteristics. Therefore*, at least 20 men (or 20%) possess all four characteristics. In the general case, if $n$ is the number of different characteristics and $p_{i}$ is the percentage of men possessing the $i$-th characteristic, then the percentage $P$ of men possessing all $n$ characteristics is given by the formula

$$
P=\sum_{i=1}^{n} p_{i}-100(n-1)
$$

[M. M., 38, 211 (September 1965).]