In how many orders can seven different pictures be hung in a row so that one specified picture is at either end?
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The number of ways the seven different pictures can be hung in a row so that one specified picture is at either end is given as follows:
After the one specified picture is hung in any one of 2 ends, the remaining 6 pictures can be arranged in 6P6 ways. Therefore the number of orders
= 2 × 6P6
= 1440 orders
Therefore, in 1440 ways, the specified picture is at either end.
If, the specified picture is at centre, then we have,
Since 1 given picture is to be at the centre, 6 pictures remain to be
arranged in a row
Therefore the number of orders = 6P6 = 6! = 720 orders
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