Question

A box contains12 balls in which 4 are white,3 blue and 5 are red.3 balls are drawn at random from the box.Find the chance that all three balls are of sifferent color.(answer in three decimal places)

Answer 1

Answer:

0.273

Step-by-step explanation:

Total number of balls is 4+3+5 = 12

There are 6 ways to draw 3 different colors (WBR, WRB, BWR, BRW, RWB, RBW) each with a chance of 4/12 · 3/11 · 5/10 = 1/22

So the total chance is 6 · 1/22 = 6/22 = 3/11 ≈ 0.273

Answer 2

$|\Omega|=_{12}C_3=\dfrac{12!}{3!9!}=\dfrac{10\cdot11\cdot12}{2\cdot3}=220\\|A|=4\cdot3\cdot5=60\\\\P(A)=\dfrac{60}{220}=\dfrac{3}{11}\approx0,273$