Tiêu đề 24 Fundamental Principle of Counting.pdf ✅

In the wardrobe example, replacement happens when the clothes picked are returned before the next selection happens. When clothes are replaced, they can be picked repeatedly. Repetition can also occur when the person has multiple pieces of clothing with a certain design. For example, How many four-digit numbers are there if the digits can be repeated? If they cannot be repeated? If the digits can be repeated (although the first one cannot be 0), then If the digits cannot be repeated, For another example, A drawer has 7 differently colored socks. A person picks two to wear. How many color combinations can be picked if the socks are replaced? If they are not replaced? If the socks are replaced, then each pick has 7 possible outcomes. The number of color combinations is 7(7) = 49. If there is no replacement, then the next pick only has 7 possible outcomes since one of the socks is already removed. The number of color combinations is 7(6) = 42. 3. By-case basis In the previous sections, the total number of outcomes is determined considering all events in the sequence that happen. However, there are situations where only some of the events happen. In these situations, the total number of outcomes is the sum of the number of outcomes of each case. For example, How many four-digit numbers are divisible by five if the digits cannot be repeated? For a number to be divisible by five, it must end in 0 or 5. The total number of outcomes is 952.