Methods of Counting
Problem 1. How many subsets are there in a set of size ?
Problem 2. Find the number of squares contained in an squares array.
Problem 3. A team is to be chosen from 4 girls and 6 boys. The only requirement is that it must contain at least 2 girls. Find the number of different teams that may be chosen.
Problem 4. You wish to give your Aunt Mollie a basket of fruit. In your refrigerator you have six oranges and nine apples. The only requirement is that there must be at least one piece of fruit in the basket (that is, an empty basket of fruit is not allowed). How many different baskets of fruit are possible?
Problem 5. Find the number of ways 30 identical pencils can be distributed among three girls so that each gets at least 1 pencil.
Problem 6. There 7 boys and 3 girls in a gathering. In how many ways can they be arranged in a row so that
1) the 3 girls form a single block?
2) the two end-possitions are occupied by boys and no girls are adjacent?
Problem 7. Between 20000 and 70000, find the number of even integers in which no digit is repeated. Continue reading “IMC training 2016 (2)”