Hello, Niko!

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Suppose the players are: from shortest to tallest.In how many ways can seven basketball players of different heights line up in a row

so that no player is standing between two people taller than she is?

We have 7 spaces to fill: . _ _ _ _ _ _ _

We note that (the shortest) canbe in the interior of the row.not

. . She will be between two taller players.

Hence, she must be on the end . . . 2 choices.

We have the other 6 players to place in 6 positions:. _ _ _ _ _ _

We note that (the shortest of this group) canbe in the interior of this row.not

. . She will be between two taller players.

Hence, she must be on the end . . . 2 choices.

And so on . . . get the idea?

[I get an answer of 64.]