Answer:
63
Step-by-step explanation:
Given that;
The bag has two red marbles, n(red) =2
three green ones marbles, n(green) = 3
one lavender one marbles, n(lavender) = 1
two yellows marbles, n(yellow ) = 2
two orange marbles. n(orange) = 2
number of non green marbles = 2+1+2+2 = 7
The objective is to find out how many sets of four marbles include exactly two green marbles
Since sets of four marbles contain exactly two green marbles, then N(select 2 from 3 marbles and 2 from 7 marbles)
= [tex]^3C_2 \times ^{7}C _2[/tex]
= [tex]\dfrac{3!}{2!(3-2)!} \times \dfrac{7!}{2!(7-2)!}[/tex]
= [tex]\dfrac{3*2!}{2!} \times \dfrac{7*6*5!}{2!(5)!}[/tex]
= [tex]3 \times 7\times 3[/tex]
= 63
