question:
You own $5$ songs by Adele, $4$ by Lady Gaga, and $3$ by Katie Perry. How many playlists can be formed that consist of $3$ Adele, $2$ Gaga, and $2$ Perry songs if (a) Repetitions are allowed (the same song may be played multiple times). (b) Repetitions aren’t allowed.
a) $5^3\times 4^2 \times 3^2 = 18 000$
b) $5^2\times 4^1\times 3^1 = 300$
Am i right?
Your answer of part $a)$ is correct, but part $b)$, it should be $\binom{5}{3}\times \binom{4}{2}\times \binom{3}{2}=180$.