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