Answer:
0.6
Step-by-step explanation:
A permutation is an arrangement of outcomes whereas a combination is a grouping of outcomes.
Order matters in case of permutations but does not matter in combinations.
Given:
Number of red marbles = 3
Number of white marbles = 2
Number of green marbles = 1
To find: probability of picking 4 marbles and getting one of each color
Solution:
Total number of outcomes = [tex]6_C__4[/tex] = [tex]\frac{6!}{4!\,2!}=\frac{6\times 5\times 4!}{4!\times 2}=15[/tex]
Number of favourable outcomes = 2 red, 1 white and 1 green marble + 1 red, 2 white and 1 green marble = [tex]3_C_2\,2_C_1\,1_C_1+3_C_1\,2_C_2\,1_C_1[/tex] = [tex]\frac{3!}{2!\,1!}\times \frac{2!}{1!\,1!}\times 1+\frac{3!}{2!\,1!}\times 1\times 1=6+3=9[/tex]
So, probability of picking 4 marbles and getting one of each color = Number of favourable outcomes/Total number of outcomes =[tex]\frac{9}{15}=\frac{3}{5}=0.6[/tex]
