find r if 11C2r=11Cr+5
Answers
Answer:
r= 2 and 5
Step-by-step explanation:
11C2r = 11Cr+5
n=11 in both c
let x = 2r and y = r+5
nCx = nCy
=> x=y and x+y=n
if x=y
=>2r=r+5
=>r=5
and if x+y=n
=>2r + r+5 = 11
=>3r=6
=>r=2
therefore r = 2 and 5
Answer: The value of r is 2 and 5.
The concept of permutation and combination can be used to solve the equation 11C(2r) = 11C(r + 5).
In combinatorics, "C" typically denotes the number of combinations. The number of combinations of "n" things taken "k" at a time is given by the formula:
C(n, k) = n! / (k! (n - k)!)
where "!" denotes the factorial function (the product of all positive integers up to that number).
Using this formula, we can rewrite the equation as:
11C(2r) = 11C(r+5)
n=11 in both combinations.
let x = 2r and y = r+5
nCx = nCy
=> x = y and x + y = n
If
x = y
=> 2r = r + 5
=> r=5
and if
x + y = n
=> 2r + r + 5 = 11
=> 3r = 6
=> r = 2
therefore,
r = 2, 5
The value of r is 2 and 5.
Learn more about permutation and combination here
https://brainly.in/question/531923
Learn more about factorial function here
https://brainly.in/question/205812
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