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How do you find the permutation or combination of 7C4 ?

Answer
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Hint: We first discuss the general form of combination and its general meaning with the help of variables. We express the mathematical notion with respect to the factorial form of nCr=n!r!×(nr)! . Then we place the values for 7C4 as n=7;r=4 . We complete the multiplication and find the solution.

Complete step-by-step answer:
The given mathematical expression 7C4 is an example of combination.
We first try to find the general form of combination and its general meaning and then we put the values to find the solution.
The general form of combination is nCr . It’s used to express the notion of choosing r objects out of n objects. The value of nCr expresses the number of ways the combination of those objects can be done.
The simplified form of the mathematical expression nCr is nCr=n!r!×(nr)! .
Here the term n! defines the notion of multiplication of first n natural numbers.
This means n!=1×2×3×....×n .
The arrangement of those chosen objects is not considered in case of combination. That part is involved in permutation.
Now we try to find the value of 7C4 . We put the values of n=7;r=4 and get 7C4=7!4!×(74)! .
We now solve the factorial values.
 7C4=7×6×5×4!4!×3!=7×6×53×2×1=35 .
Therefore, the value of the combination 7C4 is 35 .
So, the correct answer is “35”.

Note: There are some constraints in the form of nCr=n!r!×(nr)! . The general conditions are nr0;n0 . Also, we need to remember the fact that the notion of choosing r objects out of n objects is exactly equal to the notion of choosing (nr) objects out of n objects. The mathematical expression is nCr=n!r!×(nr)!=nCnr .
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