Jenny has six blouses, four different skirts, 20 different pairs of socks, and four pairs of shoes in her closet at the end of the week.
why the methods used in the previous two problems would be inefficient in determining the number of different outfits Jenny could wear..
previously:
1. In his closet, John has one red shirt, one blue shirt, one pair of shorts, one pair of jeans, and a pair of slacks.
2. John discovered that he also has a pair of boots and a pair of dress shoes in his closet.
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
The methods used in the previous two problems would be inefficient in determining the number of different outfits Jenny could wear because they only provided the count of individual items in her closet. To determine the number of different outfits, we need to consider the combinations of these items.
To find the number of different outfits Jenny could wear, we need to use the concept of permutations and combinations. This involves calculating the number of permutations for each category (blouses, skirts, socks, and shoes) and then multiplying them together to get the total number of possible outfits.
In Jenny's case, let's assume she can wear only one blouse, one skirt, one pair of socks, and one pair of shoes at a time. We will find the number of different outfits for each category and multiply them together.
1. Blouses: Jenny has six blouses to choose from. So, the number of combinations of blouses is 6C1, which is equal to 6.
2. Skirts: Jenny has four different skirts to choose from. So, the number of combinations of skirts is 4C1, which is equal to 4.
3. Socks: Jenny has 20 different pairs of socks to choose from. So, the number of combinations of socks is 20C1, which is equal to 20.
4. Shoes: Jenny has four pairs of shoes to choose from. So, the number of combinations of shoes is 4C1, which is equal to 4.
Now, we multiply the number of combinations for each category together to get the total number of different outfits:
Total outfits = Number of blouse combinations * Number of skirt combinations * Number of sock combinations * Number of shoe combinations
= 6 * 4 * 20 * 4
= 1,920
Therefore, Jenny could wear a total of 1,920 different outfits from the given items in her closet.