 Hello and welcome to the session the question says in a certain lottery 10,000 tickets are sold and 10 equal prices are awarded. What is the probability of not getting a prize if you buy A1 ticket, B2 tickets and C10 tickets? So let's start with the solution here we are given that 10,000 lottery tickets are sold in a lottery and only 10 tickets were awarded equal prices therefore we have total number of tickets sold is equal to 10,000 now 10 tickets prices are awarded minus 10 which is equal to 9,990 tickets no prizes are awarded. Let's now start with the first part where we have to find the probability of not getting a prize if you buy one ticket. Now here let us denote the event E by not getting prize if we buy one ticket. So here the number of favorable outcomes are 990 C1 and the total possible outcomes are now there are in all 10,000 tickets and we have to buy one ticket so this is the total possible outcomes. Now let us find the probability of E that is not getting a prize if you buy one ticket this is equal to number of favorable outcomes upon the total number of outcomes and this is equal to 9,990 C1 upon 10,000 C1 and this is further equal to 9,990 upon 10,000 since n C1 is equal to factorial n upon factorial 1 into factorial n minus 1 and this is equal to n into n minus 1 factorial upon factorial 1 is 1 and factorial n minus 1 and canceling we have n so the value of factorial n is n into n minus 1 into n minus 2 and so on up to 2,1 so the value of n C1 is n therefore the value of 9,990 C1 is 9,990 and 10,000 C1 is 10,000 and on canceling this comes out equal to 999 upon 1000 therefore answer to the first part as 999 upon 1000 now let us proceed on to the second part which is 2 tickets now here let us denote by not getting buying 2 tickets so the number of favorable outcomes here are is equal to 9,990 C2 hence 9,990 are the tickets on which no prize are awarded and we have to find the probability of the event of not getting a prize when we buy 2 tickets so the number of favorable outcomes are 9,990 C2 and here the total possible outcomes are 10,000 C2 since the total number of tickets are 10,000 and we have to buy 2 tickets therefore probability of event E that is not getting a prize if you buy 2 tickets is equal to number of favorable outcomes which are 9,990 C2 upon the total number of possible outcomes that is 10,000 C2 hence answer to the second part as 9,990 C2 upon 10,000 C2 now let us proceed on to the last part which is 10 tickets the event E by not getting when we buy 10 tickets so where the number of favorable outcomes is equal to 9,990 C10 since on 9,990 tickets no prize is awarded and we have to find the probability of not getting a prize when we buy 10 tickets therefore here the favorable outcomes are 9,990 C10 and the total possible outcomes is equal to 10,000 C10 there is the total number of tickets are 10,000 and we have to buy 10 tickets therefore the probability of E that is not getting a prize when we buy 10 tickets is number of favorable outcomes which are 9,990 C10 upon the total possible outcomes that is 10,000 C10 so our answer is probability of not getting a prize when we buy 10 tickets is 9,990 C10 upon 10,000 C10 so this complete cessation hope you have understood it well take care and have a good day