SOLUTION: 3 boys and 3 girls enter a room and suit randomly in roll of 6 chairs. What is the probability that they sit a) so that their gender alternates? b) so that three boys are toge

Question 1008756: 3 boys and 3 girls enter a room and suit randomly in roll of 6 chairs. What is the probability that they sit
a) so that their gender alternates?
b) so that three boys are together?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
3 boys and 3 girls enter a room and suit randomly in roll of 6 chairs. What is the probability that they sit
a) so that their gender alternates?
bgbgbg or gbgbgb
# of ways to succeed:: 2patterns*3boys*3girls*2boys*2girls*1boy*1*girl
2*3*3*2*2*1*1 = 2*9*4 = 72 ways
# of random arrangements:: 6! = 720
P(alternate) = 72/720 = 1/10
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b) so that three boys are together?
# of ways to succeed:: 4*3!*3! = 144 ways
# of random arrangements:: 720
P(3 boys together) = 144/720 = 1/5
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Cheers,
Stan H.
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