Question

When testing for current in a cable with 7 colour-coded wires, the author used a meter to test 5 wires at a time. How many different tests are required for every possible pairing of wires?

Answer 1

21 different tests are required for every possible pairing of wires.

Step-by-step explanation:

Number of colour-coded wires, i.e n = 7

Number of tested wires at a time, r = 5

By combination,

C(n, r) = n!/r! (n-r)!

n! = 7! = 7x6x5x4 3x2x1

C(7, 5) = 7!/5! (7 - 5)!

C(7, 5) = 7!/5! x 2!

C(7, 5) = 7 x 6 x 5!/5! x 2

C(7, 5) = 42/2

C(7, 5) = 21

∴ 21 different tests are required for every possible pairing of wires.