Question 746626: he James gang and Butch Cassidy's gang, each having 6 and 5 members, respectively, have gathered for the annual Bank Robbers Reunion. If the members are arranged at random for a photo, what is the probability that all the James gang will be on the left and the Cassidy gang on the right? (Set up, but do not evaluate.) Can someone please explain how I would evaluate this. Thank you.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! he James gang and Butch Cassidy's gang, each having 6 and 5 members, respectively, have gathered for the annual Bank Robbers Reunion. If the members are arranged at random for a photo, what is the probability that all the James gang will be on the left and the Cassidy gang on the right? (Set up, but do not evaluate.) Can someone please explain how I would evaluate this. Thank you.
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# of arrangements that meet the requirement:
# of ways to place each gang; 1
# of ways to arrange the James gang: 6!
# of ways to arrange the Cassidy gang: 5!
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Total # of ways to arrange the 2 gangs: and satisfy the conditions: : 1*6!*5!
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Total # of random arrangements of the combined gang menbers: 11!
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Ans: Probability you want = (6!*5!)/11! = 86400/39916800 = 0.0022
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Cheers,
Stan H.
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