If 6Cr/6pr=1/6, find the value of r.
A.1
B.3
C.5
D.6?
No idea
To find the value of r in the equation 6Cr/6Pr = 1/6, we can start by understanding what the symbols "C" and "P" represent. In combinatorial mathematics, "C" stands for combination and "P" stands for permutation.
Combination (nCr) represents the number of ways to choose r items from a set of n items, disregarding their order. Permutation (nPr), on the other hand, represents the number of ways to arrange r items from a set of n items, considering their order.
In the given equation, we have 6Cr/6Pr = 1/6. Since the denominator is the same (6), we do not need to consider it. Hence, the equation simplifies to:
6Cr/6Pr = 1
Now, to find the value of r, we need to evaluate the combinations on both sides of the equation.
6Cr/6Pr = 1
(6!)/(r!(6-r)!)/(6!)/(r!) = 1
(r!(6-r)!)/(r!) = 1
(6-r)! = 1
The only value of (6-r)! that equals 1 is when (6-r) = 0. Therefore, we can conclude that (6-r) = 0.
Solving for r, we have:
|-(6-r) = 0
|-6 + r = 0
|r = 6
So, the value of r that satisfies the equation 6Cr/6Pr = 1/6 is r = 6. Thus, the correct answer is option D.