The Coen family consists of a father, a mother, two children and a dog. A photographer is about to take the family's picture. How many different arrangements (of standing in a row) does the photographer have, if it is known that the Mother insists of standing by her younger Child, as the song says?
Answers:
A) 12	B) 24	C) 30	D) 48	E) 120
We need to find the number of arrangements of Father, Mother, Child-1, Child-2, and a Dog, so that M and C2 are always together.   Consider F and M to be one unit, then we would have total of four units: {F}, {C1}, {MC2}, {D}. The number of arrangements of these four units is 4!, but M and C2 within their unit can be arranged in 2 ways: {C2M} or {MC2}, so total number of arrangements is 4!*2=48.   Answer: 48.
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The Coen family consists of a father, a mother, two children and a dog. A photographer is about to take the family's picture. How many different arrangements (of standing in a row) does the photographer have, if it is known that the Mother insists of standing by her younger Child, as the song says?