COMBINATION

PRESENTED BY : PAYAL SHAHROLL NO . : 116MBA SEM 1 – BATCH 4COMPANY : CHAMPION TRADING

CO.

MODULE 5 PRESENTATION

CHAMPION TRADING COMPANY was established in the year 1996 by MR.HITESH SHAH who is the owner of the company.

CHAMPION TRADING COMPANY also includes its subsidiary company named SAMARTH ENTERPRISES.

The major areas in which company does trading are TOOLS,HARDWARE & PAINTS.

Champion trading company is a industrial supplier company, which supplies welding instruments & Samarth enterprise has a dealership of ASIAN PAINTS ,which includes selling of paints in wholesale and retail areas.

Company supplies it’s products in the big industries & companies like .ABB,ALSTOM,JSW,INDIAN RAILWAYS,BERGER LEWIS,COLOUR WORLD and so on

INTRODUCTION OF THE COMAPNY

WHAT IS COMBINATION ?

The number of ways in which SMALLER or EQUAL number of things are arranged or selected from a collection of things where the ORDER OF SELECTION OR ARRANGEMENT IS NOT IMPORTANT.

EXAMPLE : Selection of poker hand which is a combination of five cards selected from 52 cards.

That is , 5 things out of 52 things .

Number of combinations of ‘n’ different things taken ‘r’ at a time. Denoted by :

HERE , C = Combinations. n = No . of combinations. r = Required no. of combinations.

There are two types of combinations

REPETITION ALLOWED : SUCH AS COINS ( 5 , 5 , 10 , 10 ).

NO REPITITION ALLOWED : SUCH AS LOTTERY NUMBERS (2 , 14 , 27 , 35 ).

Let us say there are five flavors of ice cream : banana, chocolate, lemon, strawberry and vanilla. You can have three scoops. How many variations will there be?

Let's use letters for the flavors: {b, c, l, s, v}.

Example selections would be :

{c, c, c} (3 scoops of chocolate) {b, l, v} (one each of banana, lemon and vanilla) {b, v, v} (one of banana, two of vanilla)

1.Combination with repetitions

There are n=5 things to choose from, and you choose r=3 of them.Order does not matter.

WE CAN CHOOSE ANY COMBINATION FROM THIS .

2.Combinations without repetitionsLet us take the example of LOTTERY TICKETS .

This is how lotteries work. The numbers are drawn one at a time, and if you have the lucky numbers (no matter what order) you win!

LOTTERY TICKETS

COMBINATION WITH REFERENCE TO CHAMPION TRADING

COMPANY

As CHAMPION TRADING COMPANY has Dealership of ASIAN PAINTS .. So let us Understand combination with respect To ASIAN PAINTS COMBINATION.

FOLLOWING ARE THE EXAMPLES

EXAMPLE :-

Q.) A box of Asian paints contains 7 Red , 6 White , & 4 BlueCans of 2 liter each. How many selection of THREE cans can Be made so that

(a)All three are red

(b) None is red

(c) One is of each color ?

SOLUTION :- ALL THREE ARE RED

(a)All three cans will be of Red color if they are taken outOf 7 red cans and his can be done in

nCr = n! r! (n – r ) ! 7C3 = 7! = 7x6x5x4X3X2X1 = 5040 3!(7-3 )! 3! X 4! 144 *3! = 6**4!=24

(b) None of the three will be red if these are chosen from( 6 White and 4 Blue cans ) 10 cans and this can be done in

10C3 = 10! = 10! = 10x9x8x7! 3!( 10-3 ) ! 3! 7! 3x2x1x7!

= 10x9x8 3x2 = 120 ways

NONE IS RED

(c) One RED CAN can be chosen from 7 cans in 7C1 ways.

One WHITE CAN can be chosen from 6 White cans in 6C1Ways.

One BLUE CAN can be chosen from blue cans in 4C1 ways.

Hence , the number of groups of three cans such that one is Of each color = 7x6x4 = 168 ways .

ONE IS OF EACH COLOR

CONCLUSIONWe can conclude that, when the things are arrangedOr selected from a collection of things where order Of selection or arrangement is not important.

It is repetitive in nature .

We can select any combination repetitively.

THANK YOU