Question

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

Answer 1

8 C 3 = 8! / (3!(8 - 3)!) = 8! / (3! * 5!) = (8 * 7 * 6 * 5!) / (3! * 5!) = (8 * 7 * 6) / (6) = 56

56 choices.

Answer 2

Answer: 56

Explanation:

Given: An astronomer wishes to measure on a photograph the distance between the image of a certain star and three other star images nearby.

The total number of images nearby = 8

The number of images chosen by astronomer = 3

Then, the number of choices of the three stars without being in order is given by :-

`^8C_3=(8!)/(3!(8-3)!)=(8*7*6*5!)/(3!5!)=56`

Hence, he has 56 choices .