Question

1. In how many ways can 10 objects be split into two groups containing 4 and 6 objects, respectively?

2. In how many ways can a committee of 5 people be chosen out of 9 people?

3. Out of 5 mathematicians and 7 physicists, a committee consisting of 2 mathematicians and 3 physicists is to be formed. In how many ways can this be done if (a) any mathematician and any physicist can be included, (b) one particular physicist must be on the committee, (c) two particular mathematicians cannot be on the committee?

4. How many different salads can be made from lettuce, escarole, endive, watercress, and chicory?

Answer 1