How many color combinations can be obtained from 5 fluorochromes?

To determine the number of color combinations that can be obtained from 5 fluorochromes, it is essential to recognize that the problem involves selecting combinations of fluorochromes and considering the possibility of including them in varying subsets.

When dealing with combinations, the formula to calculate the total number of possible combinations of n items taken k at a time is given by the binomial coefficient, represented as C(n, k), which is calculated as n! / (k!(n-k)!). However, since the question does not limit the number of fluorochromes that can be selected (0 to 5), it is necessary to consider all subsets, including the empty set.

The total number of combinations is therefore calculated as the sum of combinations for each possible k, from 0 to n. In this case, with 5 fluorochromes, the combinations can be expressed mathematically as follows:

C(5, 0) + C(5, 1) + C(5, 2) + C(5, 3) + C(5, 4) + C(5, 5).

Calculating these,

• C(5, 0) = 1 (the empty set),
• C(5,