A bag contains four red marbles, two green ones, one lavender one, three yellows, and one orange marble. HINT (See Example 7.] How many sets of four marbles include none of the red ones?

Answer:The number of sets of four marbles include none of the red marbles= 840Step-by-step explanation:Given,Number of red marbles = 4Number of green marbles = 2number of lavender marble = 1number of yellow marble = 3number of orange marble = 1Total number of marble except red = 2+1+3+1                                                            = 7 We have to calculate the number of sets of four marbles include none of the red marbles.So,The number of sets of four marbles include none of the red marbles can be given by,[tex]N\ =\ ^7{P}_4[/tex]     [tex]=\ \dfrac{7!}{(7-4)!}[/tex]     [tex]=\ \dfrac{7!}{3!}[/tex]     [tex]=\ \dfrac{7\times 6\times 5\times 4\times 3!}{3!}[/tex]     = 7 x 6 x 5 x 4     = 840So, the total number of required sets are 840.