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If nCr denotes the number of combination of n things taken r at a time, then the expression nCr +1 + nC r -1 + 2 x nCr equals[2003]
- a)n+1Cr +1
- b)n+ 2 C r
- c)n+ 2Cr +1
- d)n+1Cr
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
If nCr denotes the number of combination of n things taken r at a time...
n Cr +1 + n Cr -1+ 2nCr = nCr -1+ n Cr + nCr + nCr +1
Most Upvoted Answer
If nCr denotes the number of combination of n things taken r at a time...
If nCr denotes the number of combinations of n things taken r at a time, then the expression nCr * (nC r-1) * 2 * nCr equals
To solve this problem, we need to simplify the given expression step by step.
Step 1: Simplifying nCr * (nC r-1)
We know that nCr = n! / (r! * (n-r)!), where "!" denotes the factorial of a number.
By substituting the values, we get:
nC r-1 = n! / ((r-1)! * (n-r+1)!)
Multiplying nCr with nC r-1, we get:
nCr * nC r-1 = (n! / (r! * (n-r)!)) * (n! / ((r-1)! * (n-r+1)!))
Step 2: Simplifying (n! / (r! * (n-r)!)) * (n! / ((r-1)! * (n-r+1)!))
To simplify this expression further, we can notice that (n-r+1)! = (n-r)! * (n-r+1).
By substituting this value, we get:
(n! / (r! * (n-r)!)) * (n! / ((r-1)! * (n-r+1)!)) = (n! / (r! * (n-r)!)) * (n! / ((r-1)! * (n-r)! * (n-r+1)))
Step 3: Simplifying (n! / (r! * (n-r)!)) * (n! / ((r-1)! * (n-r)! * (n-r+1))) * 2 * nCr
Multiplying the above expression with 2 * nCr, we get:
(n! / (r! * (n-r)!)) * (n! / ((r-1)! * (n-r)! * (n-r+1))) * 2 * nCr = 2 * nCr * ((n! / (r! * (n-r)!)) * (n! / ((r-1)! * (n-r)! * (n-r+1))))
Step 4: Simplifying 2 * nCr * ((n! / (r! * (n-r)!)) * (n! / ((r-1)! * (n-r)! * (n-r+1))))
We can observe that (n! / (r! * (n-r)!)) * (n! / ((r-1)! * (n-r)! * (n-r+1))) = n! * n! / (r! * (r-1)! * (n-r)! * (n-r)! * (n-r+1))
Simplifying further, we get:
2 * nCr * ((n! / (r! * (n-r)!)) * (n! / ((r-1)! * (n-r)! * (n-r+1)))) = 2 * nCr * (n! * n! / (r! * (n-r)! * (r-1)! * (n-r)! * (n-r+1)))
Step
To solve this problem, we need to simplify the given expression step by step.
Step 1: Simplifying nCr * (nC r-1)
We know that nCr = n! / (r! * (n-r)!), where "!" denotes the factorial of a number.
By substituting the values, we get:
nC r-1 = n! / ((r-1)! * (n-r+1)!)
Multiplying nCr with nC r-1, we get:
nCr * nC r-1 = (n! / (r! * (n-r)!)) * (n! / ((r-1)! * (n-r+1)!))
Step 2: Simplifying (n! / (r! * (n-r)!)) * (n! / ((r-1)! * (n-r+1)!))
To simplify this expression further, we can notice that (n-r+1)! = (n-r)! * (n-r+1).
By substituting this value, we get:
(n! / (r! * (n-r)!)) * (n! / ((r-1)! * (n-r+1)!)) = (n! / (r! * (n-r)!)) * (n! / ((r-1)! * (n-r)! * (n-r+1)))
Step 3: Simplifying (n! / (r! * (n-r)!)) * (n! / ((r-1)! * (n-r)! * (n-r+1))) * 2 * nCr
Multiplying the above expression with 2 * nCr, we get:
(n! / (r! * (n-r)!)) * (n! / ((r-1)! * (n-r)! * (n-r+1))) * 2 * nCr = 2 * nCr * ((n! / (r! * (n-r)!)) * (n! / ((r-1)! * (n-r)! * (n-r+1))))
Step 4: Simplifying 2 * nCr * ((n! / (r! * (n-r)!)) * (n! / ((r-1)! * (n-r)! * (n-r+1))))
We can observe that (n! / (r! * (n-r)!)) * (n! / ((r-1)! * (n-r)! * (n-r+1))) = n! * n! / (r! * (r-1)! * (n-r)! * (n-r)! * (n-r+1))
Simplifying further, we get:
2 * nCr * ((n! / (r! * (n-r)!)) * (n! / ((r-1)! * (n-r)! * (n-r+1)))) = 2 * nCr * (n! * n! / (r! * (n-r)! * (r-1)! * (n-r)! * (n-r+1)))
Step
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Question Description
If nCr denotes the number of combination of n things taken r at a time, then the expression nCr +1 + nC r -1 + 2 x nCr equals[2003]a)n+1Cr +1b)n+ 2 C rc)n+ 2Cr +1d)n+1CrCorrect answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If nCr denotes the number of combination of n things taken r at a time, then the expression nCr +1 + nC r -1 + 2 x nCr equals[2003]a)n+1Cr +1b)n+ 2 C rc)n+ 2Cr +1d)n+1CrCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If nCr denotes the number of combination of n things taken r at a time, then the expression nCr +1 + nC r -1 + 2 x nCr equals[2003]a)n+1Cr +1b)n+ 2 C rc)n+ 2Cr +1d)n+1CrCorrect answer is option 'C'. Can you explain this answer?.
If nCr denotes the number of combination of n things taken r at a time, then the expression nCr +1 + nC r -1 + 2 x nCr equals[2003]a)n+1Cr +1b)n+ 2 C rc)n+ 2Cr +1d)n+1CrCorrect answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If nCr denotes the number of combination of n things taken r at a time, then the expression nCr +1 + nC r -1 + 2 x nCr equals[2003]a)n+1Cr +1b)n+ 2 C rc)n+ 2Cr +1d)n+1CrCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If nCr denotes the number of combination of n things taken r at a time, then the expression nCr +1 + nC r -1 + 2 x nCr equals[2003]a)n+1Cr +1b)n+ 2 C rc)n+ 2Cr +1d)n+1CrCorrect answer is option 'C'. Can you explain this answer?.
Solutions for If nCr denotes the number of combination of n things taken r at a time, then the expression nCr +1 + nC r -1 + 2 x nCr equals[2003]a)n+1Cr +1b)n+ 2 C rc)n+ 2Cr +1d)n+1CrCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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If nCr denotes the number of combination of n things taken r at a time, then the expression nCr +1 + nC r -1 + 2 x nCr equals[2003]a)n+1Cr +1b)n+ 2 C rc)n+ 2Cr +1d)n+1CrCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for If nCr denotes the number of combination of n things taken r at a time, then the expression nCr +1 + nC r -1 + 2 x nCr equals[2003]a)n+1Cr +1b)n+ 2 C rc)n+ 2Cr +1d)n+1CrCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of If nCr denotes the number of combination of n things taken r at a time, then the expression nCr +1 + nC r -1 + 2 x nCr equals[2003]a)n+1Cr +1b)n+ 2 C rc)n+ 2Cr +1d)n+1CrCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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