Solution: If similar programs are not adjacent, arrange the song and dance programs of the most similar programs first.

The total number of three song and dance programs = a (3,3) = 6.

After three song and dance programs are arranged, there are four spatial positions for the arrangement of other programs.

Because three song and dance programs can't be adjacent to each other, two programs must be arranged in the middle two empty seats.

1. If two short programs are arranged in the middle two spaces, the total number of short programs is = a (2,2) =A(2.

After arranging the sketch program, there are six space positions to arrange the crosstalk program.

Then the total number of crosstalk programs is A(6, 1)=6.

Therefore, if the two vacant seats in the middle are arranged into two short programs, the total number of arrangements is =6*2*6=72.

2. If 1 sketch program and 1 crosstalk program are arranged in the middle two spaces, then the total number of arrangements = c (21) * a (2,2) = 4.

After the arrangement, the remaining sketch programs can be placed in the front and last position, so they are arranged in two ways.

Then the total number of the two vacant seats in the middle is 1 sketch program and 1 crosstalk program =6*4*2=48.

So all the permutations are =72+48= 120.

That is, there are 120 non-adjacent programs of the same kind.

Extended data:

1, classification of permutation

(1) All arrangements

When m=n in the arrangement of m different elements from n different elements, this arrangement is called complete arrangement. The number of all permutations of n elements is denoted as Pn.

(2) Selection and arrangement

When m < n, the arrangement of m different elements is called selective arrangement. The number of all permutations of n elements is expressed as P(m, n).

2. Arrangement formula

(1) total permutation formula

Pn=n*(n- 1)*(n-2)*...*3*2* 1=n！

(2) Select the arrangement formula

P(m，n)=n*(n- 1)*(n-2)*...*(n-m+ 1)=(n *(n- 1)*(n-2)*...* 3 * 2 * 1)/((n-m)*(n-m- 1)*...*3*2* 1)

=n！ /(n-m)！

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