Given:
Number of fruits = 12
kinds of fruits = 3
3 fruits are to be picked
To Find:
Find the number of ways can the fruits be picked that all the fruits be of different kind.
Solution:
As the number of fruits and the kinds of fruits are same , this means that every fruit is of different kind.
We have to select 3 different fruits from 12 different fruits.
when we select 3 different fruits from these 12 different fruits, they would be automatically be different because all are of different kind.
So we have to only select means we have to apply the combination rule.
Acc to combination rule , for selecting r articles from n articles , there [tex]nCr[/tex]
ways, therefore for selecting 3 articles from 12 articles, there would be [tex].^{12}C3[/tex] ways
= 12!/(9!x3!)
= (12x11x10)/(3x2x1)
=220
Hence the total number of ways for selecting the 3 fruits from 12 fruits would be 220.