Assume that you have 5 different types of
vegetables and 10 different types of fruit. A vegetable salad consists of a mixture of any 3 types of vegetables, and a fruit salad consists of a mixture of 2 kinds of fruit.
(1) In how many different ways can you prepare
a vegetable salad and a fruit salad?
(2) In how many different ways can you prepare
a vegetable salad or a fruit salad but not both?
(3) How many ways can you choose two different
kinds of salad?

There are 5C3 ways to prepare the vegetable salad. This is equal to 10. Further, there are 10C2 ways to prepare the fruit salad. This is equal to 45.

1. The conjunction and denotes that we multiply them. Thus, the answer is 450 ways.
2. The conjunction or denotes that we add them. The answer is 55.
3. There are 45 ways you can choose 1 fruit salad. So, there are 45 x 44 or 1980 ways to choose two different kinds of salad.

Answer Link

eudora eudora · Answer 2 · 2019-10-10T15:10:45+02:00

Answer:

1). 450

2). 55

3). 1485

Step-by-step explanation:

Out of 5 different vegetables number of ways to select 3 different vegetables = [tex]^{5}C_{3}=\frac{5!}{3!\times (5-3)!}[/tex]

= [tex]\frac{5!}{3!\times 2!}[/tex]

= 10

Out of 10 different fruits number of ways to select 2 fruits

= [tex]^{10}C_{2}[/tex]

= [tex]\frac{10!}{2!\times (10-2)!}[/tex]

= [tex]\frac{10!}{2!\times 8!}[/tex]

= [tex]\frac{90}{2}[/tex]

= 45

(1). Different ways to prepare a vegetable AND a fruit salad

= 10×45

= 450

(2). Different ways to prepare a veg salad OR a fruit salad

= 10 + 45

= 55

(3). Number of ways to choose two different kinds of salad

= [tex]^{55}C_{2}[/tex]

= [tex]\frac{55!}{53!2!}[/tex]

= [tex]\frac{55\times 54}{2}[/tex]

= 1485