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If ncr–1 = 56, ncr = 28 and ncr+1 = 8, then r is equal to
- a)8
- b)6
- c)5
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
If ncr–1 = 56, ncr = 28 and ncr+1 = 8, then r is equal toa)8b)6c...
Divide nCr - 1 and nCr ( i.e. nCr - 1/nCr = 56/28).
So after solving we get the foll. Equation. 3r = 2n + 2.
Divide nCr / nCr + 1 = 28 / 8. So we get another equation. That is 9r = 7n - 2.
Now solving these two equations we will get r = 6.
Most Upvoted Answer
If ncr–1 = 56, ncr = 28 and ncr+1 = 8, then r is equal toa)8b)6c...
Given:
ncr1 = 56
ncr = 28
ncr1 = 8
To find: The value of r
Solution:
We know that:
ncr = ncr-1 * (n-r+1) / r
Using this formula, we can write:
ncr = ncr-1 * (n-r+1) / r
And,
ncr1 = ncr-2 * (n-r) / (r-1)
We can simplify these equations by dividing them:
ncr / ncr1 = [(n-r+1) * r] / [(n-r) * (r-1)]
Substituting the given values:
28 / 8 = [(n-r+1) * r] / [(n-r) * (r-1)]
Simplifying this equation:
7/2 = r / (n-r+1)
Multiplying both sides by (n-r+1):
7/2 * (n-r+1) = r
Expanding the left side:
7/2 * n - 7/2 * r + 7/2 = r
Multiplying both sides by 2:
7n - 7r + 14 = 4r
Rearranging the terms:
7n = 11r - 14
Now, we can substitute the given values of ncr1 and ncr to get another equation:
ncr1 / ncr = r / (n-r+1)
Substituting the given values:
8 / 28 = r / (n-r+1)
Simplifying this equation:
2 / 7 = r / (n-r+1)
Multiplying both sides by (n-r+1):
2 / 7 * (n-r+1) = r
Expanding the left side:
2n / 7 - 2r / 7 + 2 / 7 = r
Multiplying both sides by 7:
2n - 2r + 2 = 7r
Simplifying:
2n + 2 = 9r
Substituting this value of 9r in the equation we got earlier:
7n = 11r - 14
We get:
7n = 2n + 2 - 14
5n = -12
n = -12/5
This is not a valid value for n (since it is not a positive integer), so we made a mistake somewhere.
Let's check the equation we got earlier:
7n = 11r - 14
We know that n = r + 1 for ncr1, so we can substitute:
7(r+1) = 11r - 14
Expanding:
7r + 7 = 11r - 14
Subtracting 7r and adding 14:
21 = 4r
r = 21/4
This is not a valid value for r either (since it is not a positive integer), so we made another mistake somewhere.
Let's check the equation we got earlier once again:
ncr / ncr1 = [(n-r+1) * r] / [(n-r) * (
ncr1 = 56
ncr = 28
ncr1 = 8
To find: The value of r
Solution:
We know that:
ncr = ncr-1 * (n-r+1) / r
Using this formula, we can write:
ncr = ncr-1 * (n-r+1) / r
And,
ncr1 = ncr-2 * (n-r) / (r-1)
We can simplify these equations by dividing them:
ncr / ncr1 = [(n-r+1) * r] / [(n-r) * (r-1)]
Substituting the given values:
28 / 8 = [(n-r+1) * r] / [(n-r) * (r-1)]
Simplifying this equation:
7/2 = r / (n-r+1)
Multiplying both sides by (n-r+1):
7/2 * (n-r+1) = r
Expanding the left side:
7/2 * n - 7/2 * r + 7/2 = r
Multiplying both sides by 2:
7n - 7r + 14 = 4r
Rearranging the terms:
7n = 11r - 14
Now, we can substitute the given values of ncr1 and ncr to get another equation:
ncr1 / ncr = r / (n-r+1)
Substituting the given values:
8 / 28 = r / (n-r+1)
Simplifying this equation:
2 / 7 = r / (n-r+1)
Multiplying both sides by (n-r+1):
2 / 7 * (n-r+1) = r
Expanding the left side:
2n / 7 - 2r / 7 + 2 / 7 = r
Multiplying both sides by 7:
2n - 2r + 2 = 7r
Simplifying:
2n + 2 = 9r
Substituting this value of 9r in the equation we got earlier:
7n = 11r - 14
We get:
7n = 2n + 2 - 14
5n = -12
n = -12/5
This is not a valid value for n (since it is not a positive integer), so we made a mistake somewhere.
Let's check the equation we got earlier:
7n = 11r - 14
We know that n = r + 1 for ncr1, so we can substitute:
7(r+1) = 11r - 14
Expanding:
7r + 7 = 11r - 14
Subtracting 7r and adding 14:
21 = 4r
r = 21/4
This is not a valid value for r either (since it is not a positive integer), so we made another mistake somewhere.
Let's check the equation we got earlier once again:
ncr / ncr1 = [(n-r+1) * r] / [(n-r) * (
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Community Answer
If ncr–1 = 56, ncr = 28 and ncr+1 = 8, then r is equal toa)8b)6c...
We are given the following equations:
We need to find the value of r.
We need to find the value of r.
Step 1: Use the property of binomial coefficients
The property of binomial coefficients states:
Substituting the values of
This simplifies to:
Step 2: Solve for n
Now, multiply both sides by 2r:
r=2(n−(r−1))
Simplifying:
r=2n−2r+2
Now, move all terms involving r to one side:
3r=2n+2
Now, we have an equation relating r and n.
Step 3: Use another property of binomial coefficients
The property of binomial coefficients also states:
Substituting the values of
This simplifies to:
The property of binomial coefficients states:
Substituting the values of
This simplifies to:
Step 2: Solve for n
Now, multiply both sides by 2r:
r=2(n−(r−1))
Simplifying:
r=2n−2r+2
Now, move all terms involving r to one side:
3r=2n+2
Now, we have an equation relating r and n.
Step 3: Use another property of binomial coefficients
The property of binomial coefficients also states:
Substituting the values of
This simplifies to:
Step 4: Solve for n
Now, cross-multiply:
2(r+1)=7(n−r)
Simplifying:
2r+2=7n−7r
Move all terms involving r to one side:
9r=7n−2
Now, cross-multiply:
2(r+1)=7(n−r)
Simplifying:
2r+2=7n−7r
Move all terms involving r to one side:
9r=7n−2
Step 5: Solve the system of equations
We now have two equations:
We now have two equations:
- 3r=2n+2
- 9r=7n−2
Solving this system of equations, we get
r=6.
Therefore, the value of r is 6.
r=6.
Therefore, the value of r is 6.
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