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6.Permutation and Combination
medium
જો $^n{C_r} = 84,{\;^n}{C_{r - 1}} = 36$ અને $^nC_{r+1}=126 $ હોય , તો $n =..........$
A
$8$
B
$9$
C
$10$
D
$5$
Solution
$\,\,\frac{{n – r + 1}}{r} = \frac{{84}}{{36}} = \frac{7}{3}\,$ અને
$\frac{{n – r}}{{r + 1}} = \frac{{126}}{{84}} = \frac{3}{2}\,\,\,\,\,$
$\frac{7}{3}r – 1 = n – r = \frac{3}{2}(r + 1)$
અથવા $14r – 6 = 9r + 9$ અથવા $ r = 3$. તેથી, $ n = 9.$
Standard 11
Mathematics
