 Hello and welcome to the session. The question says a box contains 10 red marbles, 20 blue marbles and 30 green marbles. Five marbles are drawn from the box. What is the probability that first all will be blue and second at least one will be green? First let us learn some simple ideas with the help of which we shall be solving the above problem. First is probability of an event E is given by the number of favorable outcomes, the total number of outcomes. Probability of not E is given by 1 minus probability of E and also when the number of possible outcomes are very large then the formula for calculating it is NCR where total number of outcomes and R is the total number of favorable outcomes that is the total outcomes chosen. So this is the third idea. So with the help of these few ideas which we are solving, so this is our P idea. Let us now start with the solution. Now the box contains 10 red marbles, 20 blue marbles and 30 green marbles. Therefore total number of marbles in the box is equal to 10 red marbles plus 20 blue marbles plus 30 green marbles and this is equal to 60 marbles. Now 5 marbles drawn from the box. Therefore total number of possible outcomes is equal to 60 C5. Let us now start with the first part. First we have to find the probability that all the marbles which are drawn from the box are blue. So let us denote the event E by all the marbles are blue in color. So the number of favorable outcomes is equal to the total number of marbles which are blue in color C5. Now we have to select 5 marbles. Therefore probability of the event E is given by the number of favorable outcomes that is 20 C5 upon the total number of possible outcomes which are 60 C5. That is the answer to the first part is 20 C5 upon 60 C5. Now let us proceed on to the second part. Here we have to find the probability that at least one will be green. For this let E equal to number of marbles which are not green. So this implies either they are blue in color or red in color so there are 10 red marbles and 20 blue marbles. So in all there are 30 marbles which are not green in color. Therefore the number of favorable outcomes of the event E is equal to 30 C5. That is the number of favorable outcomes that the marbles drawn are not green in color is 30 C5. Therefore probability of the event E is equal to the number of favorable outcomes that is 30 C5 upon the total number of possible outcomes which are 60 C5. Now we have to find the probability that at least one will be green. That is we have to find the probability that no marble will be green. Therefore we have to find the probability of not E. And this by our key idea is equal to 1 minus probability of E that is 1 minus 30 C5 upon 60 C5. Thus our answer is the probability that at least one will be green is 1 minus 30 C5 upon 60 C5. So this is the answer to the second part and this completes the session. Bye and take care.