In 2006 a pair of mathematicians, Nic Svenson and Piers Barnes of the Australian Commonwealth Scientific and Research Organization, determined the number of photos you needed to take of a group to ensure that one photo had everyone’s eyes open.They even won an Ig Nobel Prize in Mathematics for their work.
Severson and Barnes combined the average frequency and time of blinking with some basic statistics. It turns out the for groups less than 20, divide the number of people by three in normal light, or two in low light. So, the next time you are taking photos of a group, take a few extra photos and there is a good chance that one of them will have everyone’s eyes open.
For the more details on this calculation see Blink-free Photos Guaranteed.