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### A Sales Chart

Sarah went to a grocery shop. There is a sales chart.

 Cabbage \$1.8 for 2 Carrot \$0.6 for 1 k.g Onion \$1.75 for 1 carton Potato \$2.05 for 1 carton Tomato \$1 for 1 k.g

Sarah bought 4 carton potatoes and 1 cabbage. If she gave \$10, how much money she got back?

Hint: 10-{(4x2.05)+.9}

### The Fundamental Principle of Counting

If an event can happen in ecactly m ways, and if following it, a second event can happen in exactly n ways, then the two events in succession can happen in exactly mn ways.

Illustration.

Suppose there are five routs from A to B and three routs from B to C. In how many ways a person can go from A to C?

Since there are five different routs from A to b, the person can go the first part of his journey in 5 different ways. Having completed in any one of the 5 different ways , he has 3 different ways to complete the second part of the journey fro B to C. Thus each way of going from A to B give rise to 3 different ways of going from B to C.

There fore the total number of ways of completing the whole journey = number of ways for the first part x number of ways for the second part.
= 5 x 3=15.

Generalisation

If an event can occur in m different ways, a second event in n different ways, a third event in exactly p different ways and so on, then the total number of ways in which all events can occur in succession is mnp....

### Some defnitions of average

One of the most important objectives of statistical analysis is to get one single value that describes the characteristic of the entire mass of unwieldy data. Such a value is called central value or an average or the expected value of the variable.

The term " average " has been defined by various authors. Some important definitions are given below.

• "Average is an attempt to find one single figure to describe whole of figures" -Clark
• " An average is a single value selected from a group of values to represent them in some way-a value which is supposed to stand for whole group, of which it is a part, as typical of all the values in he group" -A.E Waugh
• " An average is a typical value in the sense that it is sometimes employed to represent all the individual values in a series or of a variable" -Ya-Lun-Chou
• "An average is a single value within the range of the data that is used to represent all the values in the series.Since an average is somewhere within the range of the data. It is also called a measure of central value" - Croxton &Cowden

### Belated New Year Wishes

I had been busy with some personal matters for the last five six weeks. In between gone for a vacation as well. But the new year day was a bit dull as my kids and I was not well after coming back from the vacation.

I wish you all a very prosperous and happy new year.

### A Problem of Combination

A box contains 12 marbles of three different colors. Green, yellow and blue- 4 each.

If you were to close your eyes and pick them at random, how many marbles must you take out to be sure that there are at least two of one color among the marbles picked out?

In the first three pickings you may get 1 of each color. in the 4 th pick there will be at least two of one color.

### Right Foot Forward

A short man takes three steps to a tall man's two steps. They both start out on the left foot. How many steps do they have to take before they are both are stepping out on the right foot together?

Ans:

Very simple.

Thirteen teachers are in Paradox, a math conference. When they arrive at the Enigma Hotel to check in, they are told that only 12 rooms are available. Since their school had made reservations for 13 rooms, the teachers are a bit upset that they will have to find another place to stay. As they are preparing to leave and find another hotel, the manager comes out and asks if there is a problem. When she hears of their situation she assures them that the Enigma Hotel has enough space to accommodate each teacher in his or her own room. She takes two of the teachers to room #1 and promises to come back in a few minutes and take one of them to another room. She takes the third teacher to room #2, the fourth teacher to room #3, the fifth teacher to room #4 and so on, taking the twelfth teacher to room #11. She then returns to room #1 and escorts the extra teacher waiting there to room #12. All of the teachers are now happily settled in their own rooms.

Is this possible? Why or why not?

O.K Here is the solution.

Actually, it is not possible. When the manager is putting the 12 th teacher in #11, the 13 th teacher is still waiting there and he or she must go to the #12 room. So, all the rooms are now occupied and in the first room there are two teachers and the teacher waiting there can not go to the #13 room.

### Just Relax

We have been discussing about serious math topics and problems for a long time. We also need some rest from that. So today we can have some math jockes.
Here we go.

Q: Why do you rarely find mathematicians spending time at the beach?
A: Because they have sine and cosine to get a tan and don't need the sun!

Q: How does one insult a mathematician?
A: You say: "Your brain is smaller than any eps1ilin >0!"

Q: How does a mathematician induce good behavior in her children?
A: `I've told you n times, I've told you n+1 times...'

Q: Why do mathematicians often confuse Christmas and Halloween?
A: Because Oct 31 = Dec 25.

Q: What does a mathematician present to his fiancee when he wants to propose?
A: A polynomial ring!

Two math students, a boy and his girlfriend, are going to a fair. They are in line to ride the ferries wheel when it shuts down.
The boy says: "It's a sin for those people to keep us waiting like this!"
The girl replies: "No - it's a cosin, silly!!!"

HAPPY HALLOWEEN!

### Find this two digit number

In a two digit number, the ten’s digit is three times the units digit.

If 36 is subtracted from the number, the digits interchange their places.
Find this two digit number.

Ans:

We can do this problem by algebraic method.
Let x be the unit's place digit.
Then the ten's place digit is 3x

Also, the number is
$10\times3x+x$
When interchanging their digits, the new number will be 10x+3x
So, when 36 is subtracted from the number,

$10\times3x+x-36=10x+3x$

$\Rightarrow31x-36=13x$

$\Rightarrow18x=36$

$\Rightarrow x=2$

That is units place digit is 2. So then's place digit is 3 times 2 =6

Therefore the number is 62.
Hope you understood this