Question

the number of ways in which 1 2 3 4 can be arranged in such a way that 3 occurs between 1 and 2 and 4 does not occur between 1 and 2 is
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Answer 1

Given:

Four numbers: 1, 2, 3 and 4

To find:

Number of ways to arrange these numbers so that  3 occurs between 1 and 2 and 4 does not occur between 1 and 2.

Solution:

Lets put 1, 2, 3 is a set and the sequence can be in two ways, i.e. 1, 2, 3 and 2, 3, 1.

Now we need to find the number of ways in which we can arrange this set and the number 4:

= 2!

And the set can be arranged in two ways, therefore total possibility = 2*2 =4

Hence, the number of ways to arrange the numbers would be 4.