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14.Probability
medium
A bag contains $3$ red, $7$ white and $4$ black balls. If three balls are drawn from the bag, then the probability that all of them are of the same colour is
A
$\frac{6}{{71}}$
B
$\frac{7}{{81}}$
C
$\frac{{10}}{{91}}$
D
None of these
Solution
(c) Required probability $ = \frac{{{}^3{C_3} + {}^7{C_3} + {}^4{C_3}}}{{{}^{14}{C_3}}}$
$ = \frac{{1 + 35 + 4}}{{14\,.\,13\,.\,2}} = \frac{{40}}{{14\,.\,26}} = \frac{{10}}{{91}}.$
Standard 11
Mathematics
