There are 6 girls and 7 boys in a class. A team of 10 players is to be selected from the class. What is the probability that a randomly chosen team has 3 or 4 girls?
First we calculate the numerator of the desired probability:
"N(___)" means "The number of ways we can choose___)
N[ (3 girls AND 7 boys) OR (4 girls AND 6 boys) ]
The word "AND" suggests MULTIPLICATION, the word "OR" suggests ADDITION:
N(3 girls)*N(7 boys) + N(4 girls)*N(6 boys)
C(6,3)*C(7,7) + C(6,4)*C(7,6) = 20*1 + 15*7 = 125
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Next we calculate the denominator of the desired probability.
That is to choose any 10 from the 13 people in the class.
That's "13 people choose 10" = C(13,10) = 286
Answer:
Edwin