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Q.

Choose whether the given statement is true or false.


nCr + nCr – 1 = n + 1Cr 


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a

True

b

False  

answer is A.

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Detailed Solution

To check: nCr + nCr – 1 = n + 1Cr
We know that,
nCr = n!r! (n-r)!
Now, LHS: nCr + nCr – 1
=n!r! (n - r)! + n!(r - 1)! (n - r + 1)!
=n!r.(r-1)! (n - r)! + n!(r - 1)! (n - r + 1)(n - r)!
 =n!(r-1)! (n-r)!1r+1n - r + 1
 =n!(r-1)! (n-r)!n - r + 1 + rr(n - r + 1)
 =n!(r-1)! (n-r)!n + 1r(n - r + 1)
 =(n + 1)!r! (n-r+1)!
=  n + 1Cr
Thus, the given statement is true.
 
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Choose whether the given statement is true or false.nCr + nCr – 1 = n + 1Cr