SOLUTION: <b> Solve using whatever counting methods are necessary. Please show work.</b> A box contains 5 red marbles and 7 black marbles. You draw 4 marbles randomly from the box. What i

Algebra ->  Probability-and-statistics -> SOLUTION: <b> Solve using whatever counting methods are necessary. Please show work.</b> A box contains 5 red marbles and 7 black marbles. You draw 4 marbles randomly from the box. What i      Log On


   

Question 35054: Solve using whatever counting methods are necessary. Please show work.
A box contains 5 red marbles and 7 black marbles. You draw 4 marbles randomly from the box. What is the probability that you will draw 3 red marbles and 1 black marble in any order?
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
A box contains 5 red marbles and 7 black marbles. You draw 4 marbles randomly from the box. What is the probability that you will draw 3 red marbles and 1 black marble in any order?
TAKING 4 MARBLES FROM TOTAL 7+5=12 MARBLES =12C4=12!/(4!)(12-4)!=12!/(4!)(8!)
=12*11*10*9/4*3*2=495
TAKING 3 RED FROM 5 RED....5C3=5!/3!2!=5*4/2=10
TAKING 1 BLACK FROM 7 BLACK....=7C1=7!/1!6!=7
NO OF FEASIBLE COMBINATIONS =10*7=70
PROBABILITY=70/495