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6.Permutation and Combination
medium
જો $^n{C_{r - 1}} = 36,{\;^n}{C_r} = 84$ અને $^n{C_{r + 1}} = 126$ ,તો $r$ મેળવો.
A
$1$
B
$2$
C
$3$
D
એકપણ નહિ.
(IIT-1979)
Solution
(c) Here $\frac{{^n{C_{r – 1}}}}{{^n{C_r}}}$ = $\frac{{36}}{{84}}$ and $\frac{{^n{C_r}}}{{^n{C_{r + 1}}}} = \frac{{84}}{{126}}$.
==> $3n – 10r = – 3$ and $4n – 10r = 6$
On solving, we get $n = 9$,$r = 3$.
Standard 11
Mathematics
