(Solved): b) A committee of 5 people is to be chosen from 6 men and 4 women. In how many ways can this be do ...

b) A committee of 5 people is to be chosen from 6 men and 4 women. In how many ways can this be done (i) if there must be 3 men and 2 women on the committee (ii) if there must be more men than women on the committee (iii) if there must be 3 men and 2 women, and one particular woman refuses to be on the committee with one particular man? c) A shop sells old video tapes, of which 1 in 5 on average are known to be damaged. (i) A random sample of 15 tapes is taken. Find the probability that at most 2 are damaged (ii) Find the smallest value of n if there is a probability of at least 0.85 that a random sample of n tapes contains at least one damaged tape.