Need some help with #3. (d) What is (n) if n for pi prime, ei e N? Question 3: T

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Need some help with #3.

(d) What is (n) if n for pi prime, ei e N? Question 3: There are 2n elephants facing each other in a circle. How many ways can they join trunks withl other elephant without their trunks crossing another pair. For example. if n= a top and bottom side, or a left and right side, but they can't pair up across the diagonals. Question 4: How many 6 digit natural numbers have no consecutive digits the same? (For example, 123456 is okay, but 122333 is not because of the 2s or 3s)

Explanation / Answer

Say 2n no of elephants facing each other in a circle. if we add all the consecutive elephants by a straight line, we'll get a polygon of 2n sides. Now if we consider the pair of elephants then we have n pair of elephants. If someone ask why pair, then a simple explanation is already given in the problem itself. On the rectangle, two adjacent points could only form a valid pair to satisfy the condition. Though the total no of pair could've been formed is 4C2 . Similarly, though 2n no of elephants can make a total pair of 2nC2 no of pairs. But the number of valid pairs can only be n as to satisfy the condition. and each pair can form a trunk joint in 1 way. hence the total no of possible way of arranging them is n*1 = n

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