SOLUTION: ) There are 5 yellow calculators, 6 black calculators and 9 blue calculators. If I grab 5 calculators at random, what is the probability that this set will include at least 3 yello

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Question 31451: ) There are 5 yellow calculators, 6 black calculators and 9 blue calculators. If I grab 5 calculators at random, what is the probability that this set will include at least 3 yellow calculators or at most 2 black calculators?
Answer by venugopalramana(3286) About Me  (Show Source):
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here are 5 yellow calculators, 6 black calculators and 9 blue calculators. If I grab 5 calculators at random, what is the probability that this set will include at least 3 yellow calculators or at most 2 black calculators?
TOTAL NOS.=5+6+9=20
SELECTIONS OF 5 =20C5
CASE 1....ATLEAST 3 YELLOW CALCULATORS.....
1...5 YELLOW............................=5C5......................=1
2...4 YELLOW AND 1 ANOTHER..............=5C4*15C1=5*15............=75
3...3 YELLOW AND 2 ANOTHER..............=5C3*15C2=(5*4/2)(15*14/2)=1050
............................................................TOTAL.=1126
CASE 2.....AT MOST 2 BLACK
1...2 BLACK AND 3 OTHERS................=6C2*14C3=(6*5/2)(14*13*12/3*2)=5460
2...1 BLACK AND 4 OTHERS................=6C1*14C4=(6)(14*13*12*11/4*3*2)=6006
3...0.BLACK AND 5 OTHERS................=6C0*14C5=1(14*13*12*11*10/5*4*3*2)=2002
..............................................................TOTAL........=13468
PROBABILITY=(1126+13468)/20C5