Mr Burke teaches a mathematics class with 15 students. In this class there are 6 female students and 9 male students. Each day Mr Burke randomly chooses one student to answer a homework question. In the first month, Mr Burke will teach his class 20 times. (a) Find the probability he will choose a female student 8 times. [2] (b) The Head of Year, Mrs Smith, decides to select a student at random from the year group to read the notices in assembly. There are 80 students in total in the year group. Mrs Smith calculates the probability of picking a male student 8 times in the first 20 assemblies is 0.153357 correct to 6 decimal places. Find the number of male students in the year group.