1.
How many ways can the letters of the word ‘APLLE’ be arrowed

2.
In how many different ways can the letters of the word 'AUCTION’ be arranged in such a way that the vowels always come together”

3.
In how many different ways can the letters of the word ‘DETAIL’ be arranged in such a way that the vowels occupy only the odd positions?

4.
In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?

5.
In how many different ways can the letters of the word 'RUMOUR’ be arranged?

6.
In how many different ways can the letters of the word ‘MATHEMATICS’ be arranged so that the vowels always come together?

7.
In how many different ways can the letters of the word 'BANKING’ be arranged se that the vowels always come together?

8.
How many arrangements can be made out of the letters of the word 'ENGINEERING’?

9.
In how many different ways can the letters of the word ‘JUDGE’ be arranged in such a way that the vowels always come together?

10.
In how many ways can the letters of the word 'LEADER’ the arranged?

__Permutations and Combinations: Essential Topics for Aptitude Test Preparation__

One of the most important and scoring section in **career aptitude test** used to be permutation and combinations. The one who knows strategy and tricks to solve these problems is likely to score well in the exam. It is all about the ordered combination of various events. If you have a clear idea about probability, it is easier to solve the event-related combinations as well. It further works as a great foundation for solving problems related to probability distributions, confidence intervals, and hypothesis testing as well.

Beginners have lots of confusions related to permutation and combination related questions. Most of the time, they find it difficult to decide which one must be used in which question and how they must be applied. Well, if you are also in the same confusion, we advise you to go through the details below. Here we have listed a few basic details about how to handle this particular section while doing **aptitude preparation**.

*Permutations:*

Let us consider an example; assume that you purchased some salad for lunch. This salad can be a mixture of tomatoes, lettuce, radishes, and carrots. But in this case, it rarely matters in which sequence these items were added into the salad; all that consumers are concerned about is the presence of all these ingredients. Whether reddish was added first or carrot, it doesn’t matter.

On the other side, let us talk about a bank account pin. Let the sequence for four-digit secret number be 7989. Now when you want to access your money at ATM, you may need to enter these four digital secret number first. But in this case, the sequence of these numbers is more important because an odd sequence will not provide access to the account.

When all such details are important for you, it defines permutation, and the order, in this case, must be precisely preserved.

*Combinations:*

This part is much easier to understand; in this case, details are not of prime importance. In the case of combinations, red-yellow-blue and yellow/red/blue appears to be the same. The permutations can be better defined as lists where orders are always important whereas combinations are some kind of groups that are not concerned about order.

Permutations, in simple words, are the best ways to arrange elements into specific sets, and one needs to follow standard guidelines to order them. The ordered arrangements can be made after studying the purpose of the list. However, in the case of combinations, you need not worry about the orders.

There are so many things in our routine life that demand knowledge about permutation and combination. However, when you are preparing for some career aptitude test, it becomes much important to solve these problems with accurate formulas.

In general, the formula for Permutation is written as:

P (n, k) = n! / (n - k)

Whereas, for combinations, the formula can be defined as:

C (n, k) = P (n, k) / k!

Candidates preparing for following competitive exams can utilize Aptitude section to improve their skills.

- Bank Competitive Exam
- MPSC Competitive Exams
- SSC Competitive Exams
- L.I.C/ G. I.C Competitive Exams
- Railway Competitive Exam
- University Grants Commission (UGC)
- NET/ SET Competitive Exam
- Common Aptitude Test (CAT)
- Career Aptitude Test (IT Companies)

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