12 Combinations Study Materials

  Combinations 

Here, the elements in some groups are to be combined, as per the given conditions. In the following example, the groups are of (a) Men, (b) Professions and (c) Musical  Instruments. As per the conditions, these are mixed and matched.


Example:

i.Five gentlemen (Mr. Ajay, Mr. Bijay, Mr. Vinay, Mr Sanjay and Mr. Akshay) are practising five different professions (Engineering, Medical, Law, Chartered Accountancy and Architecture). Each one can play only one of the five different instruments: Tabla, Violin, Sarod, Sitar and Flute.


ii.Mr Ajay is a Doctor and can play Sarod.

iii.The Sitarist is not an Engineer.

iv.Mr Vinay and Mr Bijay are not Architects and Vinay cannot play Tabla.

v.Mr Bijay can play Violin.

vi.Mr Akshay is a Lawyer and can play Flute.


Which instrument does Mr. Vinay play? AND  What is the profession of Mr. Bijay?

Solution:

Let us represent the three groups in a table. By taking the group of gentlemen as the  base, because most of the information given is with regard to the gentlemen, we will try filling in the other details/ elements of the other two groups in the table, as shown below.


From ii,            we get the combination Ajay-Doctor-Sarod.

From iii,           we get to know that Sitar ? Engineer.

From iv,           (Vinay, Bijay)  ? Architects and Vinay ? Tabla.

From v,            Bijay = Violin.

From vi,           we get the combination Akshay - Lawyer -Flute.

Putting the above details in the table as shown below.


Gentleman:-

Professional:-

Instrument:-

Gentleman:-Ajay

Professional:-Doctor

Instrument:-Sarod

Gentleman:-Bijay

Instrument:-X Architect

Professional:-Violin

Gentleman:-Vinay

Professional:-X Architect

Instrument:-X Tabla

Sanjay

 -------------

 -------------

Gentleman:-Akshay

Professional:-Lawyer

Instrument:-Flute



Now, here we observe that neither Bijay nor Vinay is the Architect; hence the remaining person Sanjay is the Architect. Similarly, Sanjay plays Tabla and hence Vinay plays Sitar. This means that Bijay is the Engineer (from iii) and Vinay is the CA. We get the final arrangement as shown below:


Gentleman:- Ajay

Professional:- Doctor

Instrument:- Sarod

Gentleman:- Bijay

Professional:- Engineer

Instrument:- Violin

Gentleman:- Vinay

Professional:- CA

Instrument:- Sitar

Gentleman:- Sanjay

Professional:- Architect

Instrument:- Tabla

Gentleman:- Akshay

Professional:- Lawyer

Instrument:- Flute


Now, based on the above table, Mr. Vinay plays Sitar AND Mr. Bijay is the Engineer.