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Permutations , combinations and binomial expansion — Statistics STD 11 Commerce — Question

Gujarat BoardEnglish MediumSTD 11 CommerceStatisticsPermutations , combinations and binomial expansion2 Marks
Question
Find the unknown value : ${ }^{27} C_{r+4}={ }^{27} C_{2 r-1}$
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Answer

${ }^{27} C_{r+4}={ }^{27} C_{2 r-1}$
${ }^n C_x={ }^n C_y$
Or
$n=x+y$
${ }^{27} C_{r+4}={ }^{27} C_{2 r-1}$
$\therefore r+4=2 r-1$
$\therefore 4+1=2 r-r$
$\therefore r=5$
Or
$r+4+2 r-1=27$
$\therefore 3 r+3=27$
$\therefore 3 r=27-3 \therefore r=\frac{27}{3}=8$

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