Redundant up-links distribution switches

I am trying to understand some basic math involved in calculating redundant up-links for access switches to distribution switches. The ICND1 depicts a diagram showing 40 access switches with 2 distribution switches with 4 up-links to each of 40 access switches resulting in 160 links.
It then goes on to say that If the design instead did not use distribution switches, to connect a single link between each pair of access switches would
require 780 links.
How was 780 calculated exactly?

Hi,
The 780 is calculated as (40 * 39) / 2.
In general, this is a question asking about the number of links needed to interconnect N nodes with a single direct link between each pair of these devices. The formula is N * (N-1) / 2, and it follows a simple logic that on each of the N nodes, you need to connect N-1 links to reach the remaining devices, and because a link connects a pair of devices, adding each link always "deals with" a pair devices, hence the division by 2.
Best regards,
Peter

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