Question

an astronomer wishes to measure on a photograph the distance between the image of a certain star and three star other star images nearby, if 8 images are nearby how many choices of the three stars does he have?

Answer 1

The astronomer has to choose 3 star images out of 8.This is a problem of combinations. This can be expressed as 8C3 i.e. combination of 8 objects taken 3 at a time.

$8C3= \frac{8!}{3!*5!}=56$

This means, if 8 images are nearby the astronomer will have 56 choices of the three stars.