Test, hurry, pencils and erasers
Mio has a big test today and she is in a hurry. For the test, she must bring at least two pencils and at least one eraser.
In her work drawer, she has pencils and erasers. Each pencil / eraser is unique. On how many ways can Mio get ready for the test?
Hints: Mio does not have to bring exactly two pencils and one eraser.
The answer is 1800.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
Solution:
For each object Mio has a choice to bring it or not to bring it (2 possibilities). So she can pick pencils on 2 7 = 1 2 8 different ways and erasers on 2 4 = 1 6 ways.
With pencils, we have 8 cases that are not satisfactory, when she doesn't pick any pencil and when she picks only one pencil. With erasers, similarly, a case where no eraser is picked is unsatisfying, that is one.
Therefore, ( 1 2 8 − 8 ) × ( 1 6 − 1 ) = 1 8 0 0