If 15 Cr r -15 C r -1-11- 5- find r-

15!/(15 r)! r!/15!/(15 r+1)!(r 1)! = 11/5 = 15!/(15 r)(16 r)!r(r 1)!/15!/(16 r)!(r 1)! = 11/5 ⇒16 r/r = 11/5 80 5r = 11r 80 = 16r r = 80/16 = 5 r = 5 ...

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Byju's Answer

Standard XII

Mathematics

Permutation: n Different Things Taken r at a Time

If 15 Cr r .1...

Question

If $^{15} C_{r} :^{15} C_{r - 1} = 11 : 5$ , find r.

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Solution

$\frac{\frac{15!}{(15 - r)! r!}}{\frac{15!}{(15 - r + 1)! (r - 1)!}} = \frac{11}{5} = \frac{15!}{\frac{(15 - r) (16 - r)! r (r - 1)!}{\frac{15!}{(16 - r)! (r - 1)!}}} = \frac{11}{5} \Rightarrow \frac{16 - r}{r} = \frac{11}{5} 80 - 5 r = 11 r 80 = 16 r r = \frac{80}{16} = 5 r = 5$

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If 15Cr:15Cr−1=11:5, find r.

15!(15−r)!r!15!(15−r+1)!(r−1)!=115=15!(15−r)(16−r)!r(r−1)!15!(16−r)!(r−1)!=115⇒16−rr=11580−5r=11r80=16rr=8016=5r=5

If $^{15} C_{r} :^{15} C_{r - 1} = 11 : 5$ , find r.

$\frac{\frac{15!}{(15 - r)! r!}}{\frac{15!}{(15 - r + 1)! (r - 1)!}} = \frac{11}{5} = \frac{15!}{\frac{(15 - r) (16 - r)! r (r - 1)!}{\frac{15!}{(16 - r)! (r - 1)!}}} = \frac{11}{5} \Rightarrow \frac{16 - r}{r} = \frac{11}{5} 80 - 5 r = 11 r 80 = 16 r r = \frac{80}{16} = 5 r = 5$