Problem: How many groups can be formed from 5 persons?
First, we represent the persons by small letters a, b, c, d, and e, and we denote a group whose members are c and d as {c, d}. We can have a group with 2 members, 3 members, 4 members, and 5 members. The members in each group are listed below. Continue reading
Amanda went shopping and bought three blouses (red, yellow, violet) and 2 skirts (blue, green) as treat for herself for her birthday. The first thing she did when she got home was tried on the skirts and blouses. Question: In how many ways can she wear them?
This problem can be easily answered by pairing each blouse to the two skirts. The red blouse can be paired with the blue or the green skirt. This is also similar to the yellow and violet blouses.
The pairing above can also be represented using a tree diagram as shown below. For each blouse, we can pair 2 skirts. Since there are three blouses, there are 3(2) = 6 possible ways to wear them. Continue reading
In Milkshakes, Beads, and Pascal’s Triangles, we have talked about a systematic way of choosing a combination of objects from a larger number of objects. Let us recall the problem in the said post.
Issa went to a shake kiosk and want to buy a milkshake. The shake vendor told her that she can choose plain milk, or she can choose to combine any number of flavors in any way she want. There are four flavors to choose from: Apple, Banana, Chico, and Durian.
In the problem, Issa can choose any number of flavors and any combination. She can choose plain milk, choose one flavor at a time, two flavors at a time, three flavors at a time, or four flavors at a time as shown in the table below (click the table to enlarge).
Notice that in writing the list, we exhausted the number of subsets in a set with four elements. If we let a, b, c, and d stand for avocado, banana, chico, and durian, and use the set notation, we can write the sets as follows: Continue reading
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