If Among 5 Children, There are 2 Siblings; in How Many Ways can the Children be Seated GMAT Problem Solving

Question: If among 5 children, there are 2 siblings; in how many ways can the children be seated in a row so that the siblings don’t sit together?

1. 38
2. 46
3. 72
4. 86
5. 96

“If among 5 children, there are 2 siblings, in how many ways can the children be seated in a row so that the siblings don’t sit together?”- 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.

Answer:

Approach Solution 1:

{The number of arrangements where the siblings do not sit together} = {The total number of arrangements of 5 children} – {The number of arrangements where the siblings sit together}
{The total number of arrangements of 5 children} = 5! = 120
{The number of arrangements where the siblings sit together}:

Consider two siblings as one unit {S1,S2}
In this case 4 units {S1,S2} {X} {Y} {Z}can be arranged in 4! Ways. Siblings within their unit can be arranged in 2 ways: {S1,S2} or {S2,S1}.
Hence the number of arrangements where the siblings sit together is 4!*2 = 48
{The number of arrangements where the siblings don’t sit together} = 120 – 48 = 72

Correct Answer: C

Approach Solution 2:

The siblings can be regarded as one unit so there are 4! Combinations
Let these siblings be S1 and S2 and others be A, B, C
So one of the arrangements out of 4! Is A, B, C, S1, S2
But we can arrange the siblings in 2 ways here
Second would be A, B, C, S2, S1
Similarly, there will be two ways for each arrangement
That’s why the number of arrangements where the siblings sit together is 4!*2 = 48

Correct Answer: C

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