Question

If ¹¹P↓(r) = ¹²P↓(r-1),find r.​

Answer 1

Answer:

Given:

The equation is,

¹¹pr=¹²p(r-1)

As we know that,

ⁿpr=n!/(n-r)!

¹¹pr=11!/(11-r)!

¹²p(r-1)=12!/(13-r)!

11!/(11-r)!=12!/(13-r)!

(13-r)!/(11-r)!=12!/11!

(13-r)(12-r)(11-r)!/(11-r)!=12×11!/11!

(13-r)(12-r)=12

156-13r-12r+r²=12

r²-25r+144=0

r²-16r-9r+144=0

r(r-16)-9(r-16)=0

(r-9)(r-16)=0

r=9

But not 16, Because 9 is satisfying the above equation....

Step-by-step explanation:

Hope it helps you........