A bag contains 5 white, 7 black and 4 red balls. Three balls... | MATH - USE OF PERMUTATIONS AND COMBINATIONS IN PROBABILITY | SolveeIt | Solveeit

Today, August 19

Question

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

A

$\frac { 3 } { 16 }$

B

$\frac { 3 } { 5 }$

C

$\frac { 1 } { 60 }$

D

$\frac { 1 } { 56 }$

Answer

$\frac { 1 } { 56 }$

Explanation

Solution

Required probability $= \frac { { } ^ { 5 } C _ { 3 } } { { } ^ { 16 } C _ { 3 } } = \frac { 5 \times 4 \times 3 } { 16 \times 15 \times 14 } = \frac { 1 } { 56 }$ .