Question

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?

Answer 1

1). 450

2). 55

3). 1485

Explanation:

Out of 5 different vegetables number of ways to select 3 different vegetables =
`^(5)C_(3)=(5!)/(3!* (5-3)!)`

=
`(5!)/(3!* 2!)`

= 10

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

=
`^(10)C_(2)`

=
`(10!)/(2!* (10-2)!)`

=
`(10!)/(2!* 8!)`

=
`(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)`

=
`(55!)/(53!2!)`

=
`(55* 54)/(2)`

= 1485