Question 260126: A researcher with the U.S. Department of Agriculture is conducting an experiment to determine how well certain crops can survive adverse weather conditions. She has gather 6 corn plants, 3 wheat plants, and 2 bean plants. She needs to select 4 plants at random for the experiment.
a) In how many ways can this be done?
b) If exactly 2 corn plants must be included, in how many ways can the plants be selected?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A researcher with the U.S. Department of Agriculture is conducting an experiment to determine how well certain crops can survive adverse weather conditions.
She has gather 6 corn plants, 3 wheat plants, and 2 bean plants.
She needs to select 4 plants at random for the experiment.
a) In how many ways can this be done?
Ans: 11C4 = (11*10*9*8)/(1*2*3*4) = 330 ways
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b) If exactly 2 corn plants must be included, in how many ways can the plants be selected?
Pick 2 corn plants: 6C2 = (6*5)/(1/2) = 15
Pick 2 non-corn plants: 5C2 = (5*4)/(1*2) = 10
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Ans: 15*10 150 ways
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Cheers,
Stan H.
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