Answer: 56
Step-by-step explanation:
Given : A bag contains five red marbles, three green ones, one transparent one, three yellow ones, and three orange ones .
Red marbles = 5
Green marbles = 3
Total marbles red or green = 5+3=8
The number of combinations of n things taking r at a time is given by :-
[tex]C(n;r)=\dfrac{n!}{r!(n-r)!}[/tex]
Then, the number of possible sets of five marbles are there in which all of them red or green is given by :-
[tex]C(8;5)=\dfrac{8!}{5!(8-5)!}\\\\=\dfrac{8\times7\times6\times5!}{5!3!}\\\\=\dfrac{8\times7\times6}{6}\\\\=8\times7=56[/tex]
Now, the number of possible sets of five marbles are there in which all of them red or green = 56
