Model: Sometimes we need to use combinations, permutations, or the Fundamental Counting Principle to calculate n(E) and n(S). For each of the following problems, use the following process: (a) Determine S and E. (b) Calculate n(S). Is repetition allowed? Does order matter? (c) Calculate n(E). (d) Compute n(E)=n(S). 1. A teacher randomly selects a group of 3 students from a class of 12 girls and 18 boys. What is the probability that all the students are girls?

2. A box contains 24 batteries, 7 of which are dead. If 5 are selected at random, nd the probability that: (a) All are dead. (b) None are dead.

3. Challenge: Some three-digit numbers, such as 101 and 313, read the same forward and backward. If you select a number from all three-digit numbers, nd the probability that it will read the same forward and backward.