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Question

In how many different ways a grandfather along with two of his grandsons and four grand daughters can be seated in a line for a photograph so that he is always in the middle and the two grandsons are never adjacent to each other.


Solution

As there are $$6$$ descendants they can be arranged in $$6!$$ ways 
Now subtracting in how many ways we can arrange the boys together $$=5!\times2!$$ ways$$.$$
Adding all the ways in the boys are together, but in the middle two possibilities$$=4!\times2!$$
$$\Longrightarrow 6!-(5!\times2!)+(4!\times2!)=528$$

Maths

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