Answer: [tex]\dfrac{1}{30}[/tex]
Step-by-step explanation:
Given : Number of apples in basket = 4
Number of peaches in basket = 3
Number of pears in basket = 4
If we randomly select and eat three pieces of fruit.
The number of ways to select an apple and the next two pieces are peaches :_
[tex]^4P_1\times ^3P_2\\\\=\dfrac{4!}{(4-1)!}\times\dfrac{3!}{(3-2)!}=4\times6=24[/tex]
The total number of ways to select 3 fruits from 10 fruits :-
[tex]^{10}P{3}=\dfrac{10!}{(10-3)!}=10\times9\times8=720[/tex]
Now, the probability that the first piece of fruit is an apple and the next two pieces are peaches will be :-
[tex]\dfrac{24}{720}=\dfrac{1}{30}[/tex]
