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Chapter 12: Q2. (page 641)

Show that Cn,n-r=Cn,r

Short Answer

Expert verified

It is proved that Cn,n-r=Cn,r.

Step by step solution

01

Step 1. Given Information.

Given to prove that Cn,n-r=Cn,r.

02

Step 2. Calculation.

When n objects are available and r are to be picked then the number of combinations is given by Cn,r=n!n-r!r!

Similarly,

Cn,n鈭�r=n!n鈭�n鈭�r!n鈭�r!Cn,n鈭�r=n!n鈭�n+r!n鈭�r!Cn,n鈭�r=n!r!n鈭�r!Cn,n鈭�r=n!n鈭�r!r!

Therefore, from the values of the expressions, Cn,n-r=Cn,r

03

Step 3. Conclusion.

Therefore, It is proved that Cn,n-r=Cn,r.

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