Question

when testing for current in a cable with seven 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? the number of tests required is

Explanation:

Step1: Identify combination formula

We use the combination formula $C(n,r)=\frac{n!}{r!(n - r)!}$, where $n$ is the total number of items and $r$ is the number of items chosen at a time. Here, $n = 7$ (total wires) and $r=5$ (wires tested at a time).

Step2: Calculate factorial values

$n!=7! = 7\times6\times5\times4\times3\times2\times1$, $r!=5!=5\times4\times3\times2\times1$, and $(n - r)!=(7 - 5)!=2!=2\times1$.

Step3: Substitute into formula

$C(7,5)=\frac{7!}{5!(7 - 5)!}=\frac{7!}{5!2!}=\frac{7\times6\times5!}{5!\times2\times1}$.

Step4: Simplify the expression

The $5!$ terms cancel out, and we get $\frac{7\times6}{2\times1}=\frac{42}{2}=21$.

Answer:

21