A bag contains three red marbles, five green ones, one lavender one, two yellows, and six orange marbles. HINT (See Example 7.) How many sets of four marbles include one of each color other than lavender? sets Nood Help? Pad W atch The

Answer:   180Step-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 haveThe 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