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**Hint:**Here, we are required to arrange the given numbers in descending order. Thus, we will start comparing the digits present in the lakhs place of the given numbers and arrange them from the largest digit to the smallest one. If the digits are the same then, the same procedure will be followed further i.e. tens thousands, thousands, hundreds, tens and units place. By this, we will be able to write the given numbers in descending order.

**Complete step-by-step answer:**

In order to arrange the given numbers in descending order, we should know that we are given four numbers which are in lakhs and the position of the commas show that these numbers are written in the Indian system of numeration.

Now, the given four numbers are: 6,00,780; 5,56,879; 6,87,340; 4,76,980

In order to write numbers in descending order, it means that we have to write the numbers from the largest to the smallest.

Since, the numbers are in lakhs, we can solve this question by first of all, looking at the digits present in the lakhs place.

Hence, we have the digits given as: 6, 5, 6, 4

Now, if we write these in descending order, then surely, the numbers with the digit 6 in the lakhs place will be written before the numbers starting from 5 and 4 respectively.

Now, the numbers with digit 6 in the lakhs place are: 6,00,780 and 6,87,340

Now, we will compare the digits at ten thousands places. The first number is having the digit 0 whereas the second number is having the digit 8 at the ten thousands place. Clearly, 8 is greater than 0.

Hence, the first number will be smaller than the second number.

Hence, we can write the given numbers in descending order as:

\[6,87,340 > 6,00,780 > 5,56,879 > 4,76,980\]

Therefore, this is the required answer.

**Hence, option C is the correct answer.**

**Note:**

There are two types of numerations to express any number or value. These are the Indian system and the international system of numeration. In the international system of expressing numbers, we have the place values of the numbers as: Ones, tens, hundreds, thousands, ten thousands, hundred thousands, million, ten million, hundred million, billion, and so on.

Whereas, if we observe the Indian system, then, we write the place values as: Ones, tens, hundreds, thousands, ten thousands, lakhs, ten lakhs, crores, ten crores, and so on.

Also, in the International system, commas are put after every 3 places starting from the units place. Whereas, in Indian system, after putting a comma after hundreds places, we put a comma after every two places.

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