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### Simple questions on combinations

Question 1)   By applying the formula for combinations, calculate the following
1. C (8, 3)
2. C (12, 6)
3. C (9, 3)

Question 2)   Find the number of combinations of
1. Five objects taken two at a time
2. Ten objects taken three at a time
3. Fifteen objects taken four at a time
Question 3)   In a class of fifty students, ten students decide to go on a trip. Solve the following:
1. Calculate the number of different groups of students that can go on the trip
2. Find out the number of different groups of students that will possibly not go on the trip
3. If two head students are chosen to go on the trip necessarily, and eight other students are to be chosen randomly, what are the number of different groups of students that can go on the trip?
Question 4)   Solve the following word problems on combinations:
1. From a class of twenty students, half are to be selected for a drawing competition. If three students agree that either they will all go in the competition together, or they will not go, find the number of different groups (combinations) of students that can be selected for the competition.
2. Determine the number of different selections of four red cards possible from a pack of 52 cards.
3. If, from a pack of 52 cards, only four are to be selected such that each of the four cards belongs to a different suite, find the number of different selections that can be made for four such cards