**Combinations in General Aptitude for GATE**

Combinations is an important topic in the General Aptitude section of the Graduate Aptitude Test in Engineering (GATE). This section evaluates a candidate's quantitative and reasoning abilities. Combinations is a branch of mathematics that deals with selecting elements from a larger set without considering the order in which they are selected.

**Understanding Combinations**

Combinations are often used to solve problems related to counting or selecting items from a group. Unlike permutations, which consider the order of selection, combinations only focus on the selection itself. For example, if we have a set of three elements {A, B, C}, the combinations of selecting two elements at a time are {AB, AC, BC}.

**Formula for Combinations**

The number of combinations of selecting r elements from a set of n elements is given by the formula:

nCr = n! / (r!(n-r)!)

Here, n! represents the factorial of n, which is the product of all positive integers less than or equal to n.

**Applications of Combinations in GATE**

Combinations are used in various types of problems in the General Aptitude section of GATE. Some common applications include:

1. Committee Formation: Problems that involve selecting a committee of a certain size from a group of individuals can be solved using combinations.

2. Probability: Combinations are used to calculate the number of favorable outcomes in probability problems. For example, determining the probability of selecting a certain number of red balls from a bag containing balls of different colors.

3. Arrangements: Combinations are used to count the number of ways to arrange objects without considering their order. This is useful in problems related to seating arrangements, formation of teams, etc.

**Tips for Solving Combinations Problems**

To solve combinations problems effectively, consider the following tips:

1. Understand the problem statement clearly and identify the given information.

2. Determine whether the problem requires the use of combinations or permutations.

3. Use the combination formula nCr to calculate the required number of combinations.

4. Simplify the expression by canceling out common terms in the numerator and denominator.

5. Use a scientific calculator or online tools to calculate factorials and perform division accurately.

By understanding the concept of combinations and practicing solving related problems, candidates can improve their performance in the General Aptitude section of GATE. It is important to practice a variety of problems to gain confidence in this topic.

Remember that the General Aptitude section carries a significant weightage in the GATE exam. Therefore, it is crucial to allocate sufficient time for preparation and practice regularly.