Answer:
a) 8
b) 15
c) 34
Step-by-step explanation:
Part a) Choices for the neck-wear
Number of regular ties = 3
Number of bow ties = 5
Total number of ties = 3 + 5 = 8
For the neck-wear any tie can be chosen among these 8 available ties. Therefore, the number of choices for the neck-wear would be 8.
Part b)
For this part we need to calculate the number of choices if both neck and bow ties are to be used.
Choosing a regular tie is independent of choosing the bow tie. According to the fundamental rule of counting, if two events are independent of each other, the number of ways of occurrence of both will be equal to the product of their individual occurrences. i.e.
Number of ways to choose both ties = Product of number of ways of choosing each tie
So,
Number of choices for wearing both ties= 3 x 5 = 15 ways
Part c)
Number of shirts = 5
Number of skirts = 4
Number of pants = 3
Number of dresses = 7
Following options are available for the outfits:
- Shirt with Skirt or Pants
- Just a dress
Number of ways to choose a pant is 3. Number of ways to chose a skirt or pant is 9.
Using the fundamental rule of counting again:
Number of ways to wear a shirt with skirt or pant = 3 x 9 = 27
Number of ways to chose a dress = 7
Therefore, we have in total 27 +7 = 34 ways of choosing the outfit.
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