1. We want to go from point A to point Z. (a) How many routes can we take if we can only move right and down? (b) How many of those routes go through the point X? (c) If we want to avoid the node X, how many routes can we take? 346 2. We want to create strings of length 12 from the English capital alphabets without repetition. If we take any of "J", "Y", "S" in the string, we must take the other two also and they must maintain their relative order (JYS). How many such strings are possible? 8 3. How many strings can be generated by using the alphabets of "EXAMINATIONS" such that all vowels don't occur together and all consonants occur together? 8 4. Suppose there are n+1 people in a city, all of whom have distinct amount of money in their account(no two person have same amount of money). Prove that there is two people among them, whose wealth difference can be evenly distributed among n people. 7 5. There are 10 people with 10 distinct height. How many ways can you arange them so that they stand in a decreasing order of height? 4