 Hello and welcome to the session. Let us discuss the following question. It says in a notary a person chooses six different natural numbers at random from 1 to 20 and if these six numbers match With the six numbers already fixed by the notary committee, he wins the prize What is the probability of winning the prize in the game? To solve this problem? We need to know The result of the combination which says that our objects and objects Can be chosen in the our ways and we also need to know the probability of any event e Which is given by the number of favorable outcomes to e Upon the total number of outcomes. So this knowledge will work as k idea Let us now proceed on with the solution Now we are given that the person chooses six numbers from The natural numbers 1 to 20 So here six numbers are to be chosen 20 so there are 20 numbers and we have to choose six numbers So six numbers out of 20 numbers can be chosen in 20 see six ways so there are 20 see six ways to choose six numbers that means there are 26 see six possibilities to Choose six numbers. So the total number of outcomes is equal to 20 see six Which is equal to 20 factorial upon? six factorial into 20 minus six factorial that is 14 factorial now simply find this becomes 20 into 19 into 18 into 17 into 16 into 15 into 14 factorial and six factorial is written as 6 into 5 into 4 into 3 into 2 into 1 into 14 factorial Simplifying this We get the total number of outcomes as 38,000 760 Now according to question we have to find the probability of winning the prize now to win the prize Person must have chosen a number which is Fixed by the lottery committee and there is only one such possibility So here E is the event of choosing a number and to win the prize. There is only one such possibility So the number of outcomes favorable to equal to one so the probability Choosing one such number is Equal to the number of outcomes favorable to E upon the total number of outcomes So the probability is one upon 38,000 760 It's the question and the session. Bye for now. Take care. Have a good day