A new addition to the family
Four siblings, Benedict, Bob, Brenda and Brian and their newborn brother, Billy, are to be seated in a row. If the probability that Billy is beside Brenda is where a and b are positive coprime integers, what is ?
The answer is 10.
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1 solution
To arrange all 5 of them, there are 5 ! ways. For Brenda and Billy to be together, we consider Brenda and Billy as one entity. Now we focus on arranging four entities so there are 4 ! ways here. Also, Brenda and Billy can exchange positions within the entity so there are a total of 2 ! × 4 ! desired outcomes. Required probability = 5 ! 2 ! × 4 ! = 5 × 4 ! 2 × 4 ! = 5 2 . So a b = 1 0 .