# Problem of the Day: 12/23/12

Out of a classroom containing 20 people, each with a different name, what is the probability that Alfred, Camellia, Edward, Grace, and Ian will be chosen by the teacher to run errands before school today? Express your answer as a common fraction.

Solution to yesterday’s problem:
For this problem I can show you two different methods: a straightforward algebraic method, and a faster method.

Method 1 – Set up an equation. $x$ will be the lowest number, $x+1$ is the next one, and so on. Our equation looks like this:
$x+(x+1)+(x+2)+(x+3)=-118$
Simplifying,
$4x+6=-118$
$4x=-124$
$x=-31$
So the consecutive numbers are -31, -30, -29, and -28. The product of -31 and -28 is 868.

Method 2 – Knowing that -118 is the sum of four numbers, we can divide -118 by four to find the average of the four numbers. -118/4 is -29.5, which must be the average of our four numbers. Since they are consecutive, we can find the two nearest integers on either side of this decimal: -30 and -31, -29 and -28. These are our four integers, and the product of the least and greatest is 868.