Question

Question
Frank and the Mathematics Teacher
One day, Frank's Mathematics teacher decides to test everyone on the
permutations topic, so he gives them a problem to work out. He gives them a
permutation of first N natural numbers and also a rule that every number should
occur only once in the permutation.
The students have to find the minimum number of steps to convert the
permutation to a new permutation according to the rule where they can only
replace a number with another number. Only Frank was able to solve the
problem, you also have to solve the problem like Frank.​

Answer 1

Answer:

1. The best method is to use the dashes. The first dash can stand for Wednesday and the second for Thursday. For Wednesday Sally can wear any of the five blouses. On Thursday she can only choose from four different blouses. Remember she can’t wear blouses on consecutive days. This gives us: 5 x 4 = 20. Answer (D).

2. The trick here is to imagine that the chemistry book is invisible. After all, it is stuck in one place so it can’t be switched around with the other books. So it’s as though we only have four books. How many ways can we arrange four books? 4! = 24  Answer (A).

3. Tyler is only choosing 1 of each article of clothing. While we could use the combination formula as the first step, whenever you are choosing for only one thing, the number of possibilities is the number you are choosing from. So if he can choose one shirt from 3 shirts, the total number of shirts he can select is 3.   Using the dash method, we can place a number in each dash: 3 x 5 x  2 = 30. Answer (C).

Explanation: