help counting

Question

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237

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In how many ways can the numbers 1 through 5 be entered once each into the five boxes below so that all the given inequalities are true?

$\boxed{\phantom{X}}>\boxed{\phantom{X}}>\boxed{\phantom{X}}<\boxed{\phantom{X}}<\boxed{\phantom{X}}$

Guest Oct 28, 2022

Melody · Answer 1 · 2022-10-29T05:36:19

The middle one must be the smallers so the middle one is 1

Now counting.

54123

53124

52134

43125

42135

32145

so I get 6 ways

LaTex for the boxes:

\boxed{\phantom{X}}>\boxed{\phantom{X}}>\boxed{\phantom{X}}<\boxed{\phantom{X}}<\boxed{\phantom{X}}

That is interesting. I shall try and remember it.