Vikram Prabhakaran

I can understand that starting a habit of reading a newspaper is little difficult so I will not ask you to do so right away. This is only for getting you highest possible marks in IBPS English section in a limited period of time. Practice Grammar, Vocabulary and Comprehension from "Objective General English" by R.S.Aggarwal. If you get stuck with grammar basics then refer "British English Grammar" by Ashok Kumar Singh.

The first n natural numbers, 1 to n, have to be arranged in a row from left to right. The n numbers are arranged such that there are an odd number of numbers between any two even numbers as well as between any two odd numbers. If the number of ways in which this can be done is 72, then find the value of n?

It needs to be visualized first that there can be only 1 odd number between any two even numbers and vice versa because if you place 3 odd numbers between 2 even numbers then some pair of even numbers will not have any odd numbers between them lets assume a set of numbers 1, 2, 3, 4, 5, 6 2, 1 ,3 ,5 ,4 ,6 not satisfying the condition thus we have only 2 of types possibility that satisfies the given condition: 1 2 3 4 5 6 2 1 4 3 6 5 the two types of possibility happened because the number of odd and number of even numbers are same but for a set of odd numbers there will be only one type of possibility i.e. starting with odd numbers. e.g.:- 2 3 4 5 1 not satisfying the condition 1 2 3 4 5 Now coming to the question. Lets suppose, n is even and thus n=2t+2 (where t is an integar with t>0) thus t+1 even numbers and t+1 odd numbers 2*(t+1)! (t+1)! = 72 (t+1)! = 6 t=2 n=6. Lets suppose n is odd and thus n=2t+1 (where t is an integar with t>0) thus t even numbers and t+1 odd numbers (2t+1)! (t)! = 72 for t=1 rhs =6 for t=2 rhs =240 thus the above equation will not be satisfied for any value of t. Hence, n = 6