You need to learn about combinations -
(1) number of ways to select 5 from 62 is;
(2) Im not sure of the question, from the 7 applicants, how many are chemists, and how many are physicists?
(4) You are choosing 4 tyres from 20. You want the probability that 1 of the chosen tyres is defective, so if you let mean not defective, and defective, then you have the following;
DNNN, NDNN, NNDN, NNND. Each of these scenarios have the same probability of occuring, so the probability of selecting 1 defective from a sample of 4 is;