Combinations - RD Sharma Solved Problems

 

What is a Combination?

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter. In combinations, you can select the items in any order.

Combinations can be confused with permutations. However, in permutations, the order of the selected items is essential. For example, the arrangements ab and ba are equal in combinations (considered as one arrangement), while in permutations, the arrangements are different.

Formula for Combination

Mathematically, the formula for determining the number of possible arrangements by selecting only a few objects from a set with no repetition is expressed in the following way:

 

 

Where:

• n – the total number of elements in a set
• k – the number of selected objects (the order of the objects is not important)
• ! – factorial

A few important results on combinations are as follows:

• The number of ways of selecting n objects out of n objects is:${}^n{C}_n=\frac{n!}{n!\left(n-n\right)!}=\frac{n!}{n!0!}=1$
• The number of ways of selecting 0 objects out of n objects is:${}^n{C}_0=\frac{n!}{0!\left(n-0\right)!}=\frac{n!}{0!n!}=1$
• The number of ways of selecting 1 object out of n objects is: ${}^n{C}_1=\frac{n!}{1!\left(n-1\right)!}=\frac{n\times \left(n-1\right)!}{\left(n-1\right)!}=n$
• ${}^n{C}_r{=}^n{C}_{n-r}$
• ${}^n{C}_r{+}^n{C}_{r-1}{=}^{n+1}{C}_r$

Indian Statistical Institute : Solved Problems

TOMATO (TEST OF MATHEMATICS AT THE 10+2 LEVELS) 

OBJECTIVE PROBLEM SOLVING

 

ISI's Test of Mathematics at 10 + 2 Level is a rigorous book for mathematics enthusiasts and for Class-12 students applying for an admission into the Bachelor of Mathematics at one of the Indian Statistical Institutes across the nation. The book provides advanced problems that are commonly found in the ISI entrance examinations and also prepares students for a study involving higher mathematics.

About the Indian Statistical Institute

ISI is an academic institute in India catering to studies in statistics. It was established in 1931 to improve the application of statistical methods across the nation. The institute provides academic programs at the undergraduate and postgraduate level in mathematics, statistics and numerical methods.

PART -1 QUESTION 1 TO QUESTION 28