Answer:

To find the value of R, we need to solve the given equations step by step. Let's break down the solution into different sections to make it easier to understand.

Section 1: Solving for NCR - 1 = 50
In this section, we will solve the equation NCR - 1 = 50 to find the value of NCR.

Given: NCR - 1 = 50

To solve this equation, we can rearrange it as NCR = 50 + 1 = 51.

Therefore, NCR = 51.

Section 2: Solving for 6NCR = 28
In this section, we will solve the equation 6NCR = 28 to find the value of NCR.

Given: 6NCR = 28

Divide both sides of the equation by 6 to get NCR = 28 / 6 = 4.67.

So, NCR = 4.67.

Section 3: Solving for CR - 1 = 8
In this section, we will solve the equation CR - 1 = 8 to find the value of CR.

Given: CR - 1 = 8

Add 1 to both sides of the equation to get CR = 8 + 1 = 9.

Therefore, CR = 9.

Section 4: Finding the value of R
Now that we have the values of NCR, CR, and NCR, we can find the value of R. Let's substitute the values into the equation NCR = (N!)/(R!(N-R)!).

Substituting the values, we have:

51C(R) = (51!)/(R!(51-R)!) = 4.67

Similarly, substituting the values for CR and NCR, we have:

9C(R-1) = (9!)/((R-1)!(9-(R-1))!) = 8

To solve this equation, we can simplify the expressions and equate them.

(51!)/(R!(51-R)!) = (9!)/((R-1)!(9-(R-1))!)

Simplifying further, we get:

(51!)/(R!(51-R)!) = (9!)/((R-1)!(10-R)!)

We can cross multiply to eliminate the factorials:

(51!)(R-1)!(10-R)! = (R!)(51-R)!(9!)

Canceling out the common terms:

51(R-1)! = R!(9!)

We can further simplify this equation:

51 = R(9)(8)(7)(6)(5)(4)(3)(2)(1)

Dividing both sides of the equation by the product of the factorials:

R = 51/9!

Calculating 9!:

9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 362,880

R = 51/362,880

Therefore, R ≈ 0.000140.

Conclusion:
After solving the given equations, we found that the value of R is approximately 0.000140.