# Permutation and combination question

## Homework Statement

A test consists of 5 pure math questions A, B, C, D, E and 6 statistics question F, G, H, I, J, K.
The examiners want to arrange all eleven questions in a random order such that a pure math question must be separated from another with exactly one statistics question

## The Attempt at a Solution

The first approach I use:

Arrange the pure math questions, in which there are 5! ways, then use the "slotting method" to slot in the Statistics question. Since there are six spaces, number of ways of slotting statistics question is 6! Hence total number of arrangement is 5!x6!

The second approach I use
Arrange the statistic questions first, in which there are 6! ways. Then slot in the pure math questions. Since pure math questions must be separated by exactly one statistic question. The number of ways of slotting is 5!x3. hence total number of arrangement is 5!x6!x3

Why is there such discrepancy?