Question

The answer according to key is A but I am unable to understand how

Answer 1

(1) Imagine the six other people standing in a line

      o   o   o   o   o   o

Now there are seven possible spots where you can put the four others

    _ o _ o _ o _ o _ o _ o _

You can put multiple of them into the same spot, for example

    A o   o BCo   o   o D o

If you condense this and compare this to some other examples

    AooBCoooDo
    ooAoBoooCD
    oABCooDooo

(2) You can see we essentially have **10 people** in a row, and we're choosing **which** of these ten people are ABCD

Answer 2

In this I am trying to mathematically resolve how to depict the required scenario of ABCD in Permutation and/or Combination as if we try to put it in cases, it would take 10!/6! cases. Thus i am trying to figure a way out to represent the cases using P&C but I can't figure a way to do it. Other than that it is simple to fill the gaps with 6 people by Permutation but I am unable to figure out a way to put the ABCD restriction and as a result I am unable to solve the question.

Answer 3

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