Answer: 180
Step-by-step explanation:
Given : A bag contains three red marbles, five green ones, one lavender one, two yellows, and six orange marbles.
The number of ways to choose one thing out of n is given by:-
[tex]^nC_1=\dfrac{n!}{1!(n-1)!}=n[/tex]
Number of ways to choose one red marble out of 3= [tex]^3C_1=3[/tex]
Number of ways to choose one green marble out of 5= [tex]^5C_1=5[/tex]
Number of ways to choose one yellow marble out of 2= [tex]^2C_1=2[/tex]
Number of ways to choose one orange marble out of 6= [tex]^6C_1=1[/tex]
By using the Fundamental counting principle , we have
The number of sets of four marbles include one of each color other than lavender will be :-
[tex]3\times5\times2\times6=180[/tex]
Hence, the number of sets of four marbles include one of each color other than lavender =180
