# (i) If 20Cr = 20Cr+6, find r.(ii) If 18Cr = 18Cr+2, find rC5.

Given: 20Cr = 20Cr+6

To find: r=?

We know that:

nCr = nCn-r

20Cr+6= 20C20-(r+6)

20Cr+6= 20C20-r-6=20C14-r

20C14-r= 20Cr

14-r=r

2r=14 Ans:r=7

ii) Given: 18Cr = 18Cr+2

To find: rC5=?

We know that:

nCr = nCn-r

18Cr+2= 18C18-(r+2)

18Cr+2= 18C18-r-2=18C16-r

18C16-r= 18Cr

16-r=r

2r=16 So,

rC5= 8C5

8C5= 8C5= 8C5= 8C5= 8C5= 8C5=56

Ans: 8C5=56

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