Seven people leave their bags outside a temple and returning after worshiping picked one bag each at random. In how many ways exactly three of them get their own bags?

Q. Seven people leave their bags outside a temple and returning after worshiping picked one bag each at random. In how many ways at least one and at most three of them get their correct bag?

Q. Seven people leave their bags outside a temple and returning after worshiping picked one bag each at random.In how many ways atleast one and atmost three of them get their correct bags?

Q. If you have 2 bags & 3 water bottles, then in how many ways you can choose each one of them ........

Q. If you have 2 school bags and 3 water bottles then, in how many different ways can you choose each one of them, while going to school?

Q. I have three bags that each contain $100$ marbles- Bag $1$ has $75$ red and $25$ blue marbles, Bag $2$ has $60$ red and $40$ blue marbles, Bag $3$ has $45$ red and $55$ blue marbles. I choose one of the bags at random and then pick a marble from the chosen bag, also at random. What is the probability that the chosen marble is red?