Answer: 0.33333
Step-by-step explanation:
Given: Number of Vegetable side dishes = 3
Number of Fruit side dishes = 2
Number of Grain-based side dishes = 5
Thus, the total number of side dishes =[tex]3+2+5=10[/tex]
Now, the number of ways for choosing two side dishes from total 10 dishes will be :
[tex]^{10}C_2=\frac{10!}{(10-2)!2!=45}[/tex]
Then the number of ways to randomly choose one vegetable and one grain-based side dish is given by :-
[tex]^{3}C_1\times^{5}C_1=3\times5=15[/tex]
Thus, the probability of randomly choosing one vegetable and one grain-based side dish =[tex]\frac{15}{45}=\frac{1}{3}=0.33333333...\approx0.33333[/tex]
