Question

f four marbles are to be picked at random, in how many ways could we pick

One marble for each color.

All the green marbles

3 of the green marbles

Answer 1

In a box, there are 3 red marbles,4 green marbles, 2 blue marbles and 5 yellow marbles

number of ways we could pick one marble for each color:

$n=3\cdot4 \cdot2\cdot5=120$

number of ways such that all the green marbles:

$n=C^4_4=1$

number of ways such that 3 are the green marbles:

$n=3+2+5=10$ (number of not green marbles)