 Hello friends, welcome to the session I am Shashi and I am going to help you with the following question. Question says the probability that a student is not a swimmer is 1 upon 5 then the probability that out of 5 students 4 are swimmers is we have to choose the correct answer from A, B, C and D. Let us now start with the solution. Let us assume that x denote number of swimmer students in 5 students. Now the repeated selections of students are Bernoulli trials, we know Bernoulli trials are finite in number, they are independent, they have exactly 2 outcomes success or failure and probability of success remains same in each trial. Now since event of selecting student is independent and number of trials is definite that is 5, so the trials that is repeated selection of students are Bernoulli trials. Now x has binomial distribution with n is equal to 5 and p is equal to 4 upon 5, we know n represents the total number of trials that is 5 and p is the probability that a student is a swimmer. Now we are given that probability that student is not a swimmer is 1 upon 5, so probability that a student is a swimmer is equal to 1 minus 1 upon 5 which is further equal to 4 upon 5. Now probability that student is not a swimmer is represented by q it is equal to 1 upon 5. Now we know probability of x successes is equal to n c x multiplied by q raise to the power n minus x multiplied by p raise to the power x where x is equal to 0, 1, 2, till n. Now we know x represents the number of swimmer students in 5 students. Now probability of 4 swimmer students in 5 students is represented by p x is equal to 4 which is further equal to 5 c 4, you know n is equal to 5 value of x is equal to 4, here value of q is 1 upon 5 and n minus x is equal to 5 minus 4 that is 1 and value of p is 4 upon 5 and here we will substitute value of x that is 4. Now this is further equal to 5 c 4 1 upon 5 multiplied by 4 upon 5 raise to the power 4. What we can write it as 5 c 4 4 upon 5 raise to the power 4 multiplied by 1 upon 5. So probability that out of 5 students 4 are swimmers is given by this expression. So our correct answer is a, so this is our required answer, this completes the session, hope you understood the solution, take care and have a nice day.