Mathematics: 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?

28x20=5607x3=21560-21=539539*2=269.5...

Assume that you have 5 different types of vegetables

kiylabeasty7302

06.01.2022

1). 450

2). 55

3). 1485

Step-by-step explanation:

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

= $\frac{5!}{3!\times 2!}$

= 10

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

= $^{10}C_{2}$

= $\frac{10!}{2!\times (10-2)!}$

= $\frac{10!}{2!\times 8!}$

= $\frac{90}{2}$

= 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

= $^{55}C_{2}$

= $\frac{55!}{53!2!}$

= $\frac{55\times 54}{2}$

= 1485

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