If the numbers 1,2,3….,n are arranged in a line at random what is the probability that the numbers 1 and 2 will appear next to each other?

The numbers 1,2,3,..n are arranged in a random order. The probability that the digits 1,2,3,….k (k lt n) appear as neighbours is

If the letters of the word MOTHER are arranged at random then find the probability that the vowels will be next to each other.

The numbers 1,2,3,.., n are arranged in a random order. The probability that the digits 1,2,3,..,k(n gt k) appears as neighbours in that order is

The numbers 1,2,3,…n are arranged in a random order. The probability that the digits 1,2,3,…..,k( k lt n ) appear as neighbours in that order is

The numbers 1,2,3,.., n are arranged in a random order. The probability that the digits 1,2,3,..,k(n gt k) appears as neighbours in that order is

The numbers 1,2,3,.., n are arranged in a random order. The probability that the digits 1,2,3,..,k(n gt k) appears as neighbours in that order is

The numbers 1,2,3,.., n are arranged in a random order. The probability that the digits 1,2,3,..,k(n gt k) appears as neighbours in that order is

The numbers 1,2,3,.., n are arranged in a random order. The probability that the digits 1,2,3,..,k(n gt k) appears as neighbours in that order is

The numbers 1,2,3,.., n are arranged in a random order. The probability that the digits 1,2,3,..,k(n gt k) appears as neighbours in that order is a. ((n-k)!)/(n!) b. ((n-k+1)!)/(.n!) c. (n-k)/(,^nC_k) c. (k!)/(n!)

From 100 tickets numbered 1,2,3,......,100, four are drawn at random.What is the probability that 2 of them will bear numbers from 1 to 40 and the other 2 will bear any number from 41 to 100?