SOLUTION: The number of arrangements that can be formed by taking all the letters of the word CHEESE so that no two Es come together

There are only 4 basic ways that no two Es come together.
They are

1.   _ E _ E _ E

2.   E _ _ E _ E

3.   E _ E _ _ E

4.   E _ E _ E _

where the letters C, H and S fill the blanks.

For each of those 4 ways we can arrange the C, H and S
in the 3 blanks in 3! ways.

Answer (4)(3!) = (4)(6) = 24 ways.

Edwin