Question

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

Answer 1

Answer:

56 different tests

Step-by-step explanation:

Given:

Number of wires available (n) = 8

Number of wires taken at a time for testing (r) = 5

In order to find the number of different tests required for every possible pairing of five wires, we need to find the combination rather than their permutation as order of wires doesn't disturb the testing.

So, finding the combination of 5 pairs of wires from a total of 8 wires is given as:

$^nC_r=\frac{n!}{r!(n-r)!}$

Plug in the given values and solve. This gives,

$^8C_5=\frac{8!}{5!(8-5)!}\\\\^8C_5=\frac{8\times 7\times 6\times 5!}{5!\times 3\times2\times1}\\\\^8C_5=56$

Therefore, 56 different tests are required for every possible pairing of five ​wires.