# 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?

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where does the x3 come from?

When I arrange the six statistics questions, there will be 7 spaces to slot in the 5 pure maths questions. Since there is the restriction that pure math question must be followed by exactly one statistics question, there are three ways to arrange 5 questions in these 7 free spaces. If there is no restriction, the number of ways of arranging pure math questions would be 7p5

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Homework Helper
I'm afraid there's only 5 spaces to slot in 5 pure math questions.
If you use your first or last slot, you're left with 5 spaces between statistics questions for which you have only 4 questions left.