A bag contains 5 white,7 black,and 4 red ball | vedclass

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(D) Total number of balls in the bag $= 5 + 7 + 4 = 16$.We need to draw $3$ balls out of $16$. The total number of ways to select $3$ balls is given b

Vedclass · Accepted Answer

$\frac{1}{56}$

Vedclass · Answer

(D) Total number of balls in the bag $= 5 + 7 + 4 = 16$.We need to draw $3$ balls out of $16$. The total number of ways to select $3$ balls is given by $^{16}C_3 = \frac{16 	imes 15 	imes 14}{3 	imes 2 	imes 1} = 16 	imes 5 	imes 7 = 560$.The number of ways to select $3$ white balls out of $5$ white balls is given by $^{5}C_3 = \frac{5 	imes 4 	imes 3}{3 	imes 2 	imes 1} = 10$.The probability of drawing $3$ white balls is $P = \frac{	ext{Number of favorable outcomes}}{	ext{Total number of outcomes}} = \frac{10}{560} = \frac{1}{56}$.

$A$ bag contains $5$ white,$7$ black,and $4$ red balls. Three balls are drawn from the bag at random. The probability that all the three balls are white is:

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