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**differentiate** Q2. An eyebrow is an arrangement of the numbers 1,2,3,4 and 5 such that the second and fourth numbers are each bigger than both their immediate neighbours. For example, (1,3,2,5,4) is an eyebrow and (1,3,4,5,2) is not

the number 5 can be in the 2nd and 4th position since it's the largest number. when this occur.

when 5 is in the 2nd position, 4 must be in 4th position.

_ 5 _ 4 _

that's 3! = 6 ways

or vice versa = 6 x 2 =12 ways

or the 4th position could be occupied by 3, providing that the number 4 is not next to 3.

_ 5 _ 3 _

4 has two places to go. and the remaining has 1. hence 2 x 1 = 2 ways

and you can also have the alternate, where 3 sits in the 2nd position. hence 2 x 2 = 4 ways

Total = 4 +12 = 16 ways