Question

If 18cr=18cr+2then rc5 and find the vlaue of Cr5

Answer 1

18C18-r = 18Cr+2

comparing

18-r = r+2

r = 8

8c5

= 56

Answer 2

Answer:

$^rC_{5}=56$

Step-by-step explanation:

We know that,

$If\: ^nC_{r}=^nC_{p}\: then\\r=p \:Or \:r+p=n$

$Now,\\ i) ^{18}C_{r}=^{18}C_{r+2}$

$\implies r+p =n$

$\implies r+r+2=18$

$\implies 2r = 18-2$

$\implies 2r=16$

$\implies r =\frac{16}{2}=8$

$ii) ^rC_{5}= ^8C_{5}\\=\frac{8!}{5!(8-5)!}$

$Since , \boxed {^nC_{r}=\frac{n!}{r!(n-r)!}}$

$=\frac{8\times 7\times 6\times 5!}{5!3\times 2\times 1}\\=56$

Therefore,

$^rC_{5}=56$

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