Day 5 examples
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(1) Combinations refer to arrangements where order does not matter, unlike permutations where order does. (2) The formula for calculating the number of combinations of n things taken r at a time is nCr = n! / (n-r)!r!. (3) Examples where order does not matter include card hands, lottery numbers, and committees.
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- 3. Ex) From a group of 5 students, 3 will be chosen to work on a grad committee. (a) How many different committees of 3 are possible? (b) If Amanda, one of the students, has to be on the committee, how many are possible?
- 4. Ex) A cribbage hand consists of 6 cards (a) How many different hands are possible? (b) How many hands with 3 kings only are possible? (c) How many hands with 2 or more kings?
- 5. Ex) A class has 15 girls and 20 boys. (a) How many committees of eight consisting of 3 girls and 5 boys can be made? (b) If Jill, Melissa, and Adam must be on the committee? (c) A committee of 5 with at least 3 girls?