Question: 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 know that the father insists of standing by his woman, as the song says?

1. 12
2. 24
3. 48
4. 60
5. 120

Answer:

Solution with Explanation:
Approach Solution (1):

F, M, C1, C2, D (let those be Father, Mother Children1, Children 2 and Dog respectively)

We need to find all the variations for:

F, M, X, X, X ---> the arrangements for the three spots is 3!, so 6 options. Also need to consider the other 6 options when mother is at postion one and father at 2. So in total 12.
X, F, M, X, X = the same
X, X, F, M, X = the same
X, X, X, F, M = the same

The total number of variations would be 12 * 4, which is 48.

Correct Option: C

Approach Solution (2):

We need to find the number of arrangements of Father, Mother, Child-1, Child-2, and a Dog, so that F and M are always together.

Consider F and M to be one unit, then we would have total of four units: {FM}, {C1}, {C2}, {D}. The number of arrangements of these four units is 4!

But F and M within their unit can be arranged in 2 ways: {FM} or {MF}, so total number of arrangements is 4! * 2 = 48

Correct Option: C

Approach Solution (3):

Family has five members.

Two members (mother and father) must be next to each other. So, we should consider them as one member, who can be arranged in two variations (mother and father; father and mother).

Now we have four members and four sports for them ___.

The first spot can take 4 members, the second- 3, the third- 2, and the last- 1.

It will be 4 * 3 * 2 * 1 = 4! = 24 arrangements, but we should remember that our “unique” member (which includes mother and father) can be in two variations, so 24 * 2 = 48.

Correct Option: C

“The Coen family consists of a father, a mother, two children, and a dog GMAT Problem Solving”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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