Learn about Combination and Remainder

combination and remainder

What do you mean by Combination?

A combination is one of the easiest terms in mathematics. A little bit of practice and some mathematical techniques will master you in doing combinations. By definition, it is a selection of some items from a group in a way that the order of collection doesn’t matter. 

You can collect different numbers from different groups and assign them to a separate group. It will be called the combination of those numbers. 

For example, if you are having a fruit salad you will select three fruits from three baskets that contain many fruits. You have selected mango, apple, and banana. It does not matter what is the order of fruits. It will remain the same.  But you have successfully made a combination group (fruit salad) 

“Combinatorics” is a branch of mathematics in which you study combination and permutation. In combination, you have no concern with the order of numbers but in permutation, you have to be aware of the order. 

Types of combinations

There are two types of combinations.

  • Repetition is allowed E.g the coins in your wallet (2, 5, 5, 2, 1)
  • Repetition is not allowed. E.g The prize bond numbers (11, 23, 12) (23, 34, 54) (21, 87 ,88) 

Combination without repetition and repetition

In both types, the order does not matter. If we have considered the second type in which (repetition is not allowed) it is the order on which lottery works. You can pick different numbers from the lottery but only a specific number with specific combinations will be lucky. You can not repeat the order of your selected number to win. 

What is a combination formula?

The combination formula nPr reveals the number of combinations without repetition of “n” things taken “r” at a time.

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

By using the above formula, You can calculate combinations but if you want to avoid the small blunders in the manual calculation you can simply use the combination math calculator. It will provide you the most trustable and accurate results in a split second. 

What is remainder?

The remainder is the amount or number which is “leftover” after doing some calculations. The concept is basic for all terms. For example, in arithmetic remainder is the integer which “leftover” when we divide one integer by another to make an integer quotient called integral division. 

Similarly, in algebra, it is the polynomial that is “leftover” after dividing one polynomial by another. There is an operation called modulp operation it produces such a remainder when given a dividend and divisor. 

More precisely it is called the “difference”. It is a number left after subtracting two items. 

Properties of remainder

There are some properties of the remainder which is stated below:

  • When two numbers divide each other completely the remainder will be 0
  • The divisor is always larger than the remainder. If you find a remainder greater than the divisor, it shows that division is still incomplete.
  • The remainder can be greater or less than the quotient. For example, when you divide 41 by 7 the remainder is 6 and the quotient is 5. Here the quotient is smaller than the remainder. 

Let’s consider another example, 19 could not be divided exactly by 5.

The closest will be 5*3=15 and 4 as the remainder. And the answer will be written as “3 with the remainder of 4”. It shows that 19 can 19 is divided by 5 into three parts but with 4 leftovers. i.e remainder. And it will be written as “3 R 4”

How to find the remainder?

The reminder can be found manually. I,e simply solved it in a paper. But it is simple only when the divisor and dividend are small numbers. When you have a deal with large numbers division becomes complex. At this point use technology and take help with the remainder finder. You only need to put the dividend and divisor in bars. Press calculate and you’ll get your answer.