【Example 8】There are 10 programs, 6 of which are singing and 4 are dancing, and it is required that at least 1 singing program is arranged between every two dancing programs.

Different ways: Then, from the 5 intervals created by these singing programs and the positions at the very beginning and end, a total of 7 possible positions, choose 4 to insert the dancing programs, which ensures that there is at least one singing program between every two dancing programs. There are $A_{7}^{4}$ different ways to do this. Therefore, there are a total of $A_{6}^{6} \cdot A_{7}^{4}$ different ways to arrange the order of the programs.
Example 8 Solution First, arrange the 6 singing programs in order, there are $A_{6}^{6}$ ways

to do this.