Question

What do N and R stand for in combination?

Answer 1

Hint: If there is a question in which we have to choose some number from a given number and the order is not specified, then that type of question will be solved with the help of a combination. So the formula of permutation and combination should be known to us. Only then the question will be solved.

Complete step-by-step solution:
A Combination is a kind of technique in mathematics that determines the number of possible arrangements in a collection of items where the order does not matter in the selection. The main thing about combination is that we can select items in any order.
There is one more thing in mathematics other than combination, which is known as permutation. A Permutation is also a kind of technique in mathematics that determines the number of possible arrangements in a set where the order matters in the selection. The items have to be selected in a particular order in permutation.
So here we have to know about N and R that are present in the formula of combination. So according to the formula of combination.
\[{}^{n}{{C}_{r}}=\dfrac{\left| \!{\underline {\,
  n \,}} \right. }{\left| \!{\underline {\,
  r \,}} \right. \left| \!{\underline {\,
  n-r \,}} \right. }\]
  Where,\[\left| \!{\underline {\,
  n \,}} \right. =n\times (n-1)\times (n-2)\] and so on
  \[\dfrac{\left| \!{\underline {\,
  16 \,}} \right. }{\left| \!{\underline {\,
  3 \,}} \right. \left| \!{\underline {\,
  16-3 \,}} \right. }\]
‘n’ represents the number of things that we have to choose from and ‘r’ represents the number of things that we choose from ‘n’
No repetition will be there and the order does not matter in this combination.
For example: if we have a question that we have to choose \[3\] balls from \[16\] balls, then how many possibilities will there be and the order is not specified, then this question will be solved with the help of a combination.
So how many possibilities will be there will be given by this formula, as shown below
   \[{}^{16}{{C}_{3}}\]=\[\dfrac{\left| \!{\underline {\,
  16 \,}} \right. }{\left| \!{\underline {\,
  3 \,}} \right. \left| \!{\underline {\,
  16-3 \,}} \right. }\], so the number of possibilities of selecting a ball can be found with the help of this formula.
Where, \[16\] is the total number of possibilities we have to choose from and it is given by ‘n’ and \[3\]is the number that we have to choose from \[3\] and it is given by ‘r’.


Note: There are two types of combination, one in combination with repetition and the other one is combination without repetition. There are various applications of permutation and combination. The list of arrangement of books on a shelf is an example of a permutation. When we pick multiple things at the same time then it is an example of the combination.