I am attaching pictures of the questions below.

Questions: 1. There are 10 candidates applying for 4 positions at an engineering rm. (a) How many ways are there to rank, in order, all 10 candidates? (b) How many ways are there to rank, in order, the top 4 candidates? (c) How many ways are there to choose 4 candidates from the 10'? (d) Ii" the candidates consist of 7 candidates from public schools and 3 candidates from private schools, how many ways are there to choose 2 candidates from a public school and 2 candidates from a private school? 2. In testing a certain kind of truck tire over rugged terrain, it is found that 31% of the trucks fail to complete the test run without a blowout. Of the next 20 trucks tested, nd the probability that (Hint: Binomial Distribution) (a) fewer than 5 have blowouts; (b) from 3 to 7 (inclusive) have blowouts. 3. In an experiment, the number of radioactive particles that pom through a counter follows a Poisson process with an average of 3.2 per millisecond. (a) What is the probability that exactly 2 particles pass through the counter in a milli- second? (b) What is the probability that at least 2 particles pass through the counter in a milli- second? (c) If T is the time until the next particle passes through the counter. what is P(T b 0.5) (Hint: Emuential Distribution}? 4. Suppose P(X > k) = 0.025. Find 1: if (a) X has a standard normal distribution. (b) X has 1! distribution with 18 degrees of freedom