Case of 3 Identical Notebooks

Three people all set down their identical notebooks on a table. On the way out, they each randomly pick up one of the notebooks. What is the probability that none of the three people pick up the notebook that they started with?

That's correct probability!

Probability in Case of 3 Identical Notebooks

What was the case?

Let's name peoples as Person - 1, Person - 2, Person - 3 and their notebooks as Notebook - 1, Notebook - 2 and Notebook 3 respectively.

Now there can be 6 ways 3 notebooks can be distributed among 3 persons like below.

(Here, for convenience, 3 different colors are assigned to the notebooks of 3 persons.)

As we can see, there are only 2 cases, where the each of person not getting own notebook. In rest of cases, at least 1 person got own notebook & notebooks of others are shuffled between 2.

So the probability that none of the three people pick up the notebook that they started with is 2/6 = 1/3. 

The Shopping Challenge

At a stationary shop, shopkeeper sells notebook at Rs.15, Pen at Rs.1 & Eraser at Rs.0.25. You are asked to purchase 100 objects & you are given Rs.100 note. 

So how many notebooks,pens & erasers would you buy?

Shopping Challenge

Here is what should you do! 

Taking The Shopping Challenge

What was the problem?

Let N = number of notebooks, P = number of pens & E = number of erasers.

From the given maths we get 2 equations as,

N + P + E = 100................(1)

15N +1P +E/4=100…....(2)
 
From (1),

P = 100 - N - E

From (2),

60N + 4P + E= 400

60N + 4(100-N-E) + E = 400

60N + 400-4N-4E + E = 400

56N - 3E = 0

56N = 3E

N/E = 3/56

From the ratio, we get, N=3, E=56.

Putting these in equation (1),

We get,

P=41.

So we should buy 56 erasers,41 pens & 3 notebooks to satisfy the given condition.