Question

A florist sells roses in five different colors.

a) How many bunches of a half-dozen roses can be formed?

Answer: 5^6

b) How many bunches of a half-dozen can be formed if each bunch must contain at least one rose of each color?

Answer: 5x4x3x2x1x5

Are my answers correct? If not, then can you please give me a hint?

Thanks in advance

Answer 1

The questions state that the roses are in bunches. This indicates that combinations, not permutations, are required. If permutations were required then some term like 'arrangements' (where the order is important) would have been used.
The number of combinations of n different things, taken k at a time, with repetitions is given by:
\[\left(\begin{matrix}n+k-1 \\ k\end{matrix}\right)\]
The number of combinations of five roses in the bunch can be found from the formula above. There are 5 different ways of supplying the sixth rose for each of the number of combinations of five.