If you want to find the number of ways to string 8 different types of flowers in a line (i.e., arrange them in order), the total number of ways is given by the number of permutations of 8 distinct items:

8!=8×7×6×5×4×3×2×1=40,3208!=8\times 7\times 6\times 5\times 4\times 3\times 2\times 1=40,3208!=8×7×6×5×4×3×2×1=40,320

So, there are 40,320 ways to arrange 8 different flowers in a sequence. Additional context if forming a garland (circular arrangement): If the flowers are strung to form a circular garland (where rotations are considered the same arrangement), the number of distinct ways to arrange 8 different flowers is:

(8−1)!=7!=5,040(8-1)!=7!=5,040(8−1)!=7!=5,040

because in a circle, one position is fixed to avoid counting rotations as different. Special case: If 4 particular flowers must always be together If you want to arrange 8 flowers so that 4 particular flowers are always together (treated as one block), the number of ways to arrange them in a garland is:

4!×4!2=288\frac{4!\times 4!}{2}=28824!×4!​=288

Here, the 4 particular flowers can be arranged among themselves in 4!4!4! ways, and the remaining 5 entities (the block + 4 other flowers) can be arranged in 4!/24!/24!/2 ways accounting for garland symmetry (flipping)

Summary:

Scenario| Number of ways
---|---
Linear arrangement of 8 different flowers| 8!=40,3208!=40,3208!=40,320
Circular garland arrangement of 8 flowers| (8−1)!=7!=5,040(8-1)!=7!=5,040(8−1)!=7!=5,040
Circular garland with 4 particular flowers always together| 4!×4!2=288\frac{4!\times 4!}{2}=28824!×4!​=288

This covers the general and special cases of arranging 8 different flowers.