Question

Consider a bag containing five red marbles, three green ones, one transparent one, three yellow ones, and three orange ones How many possible sets of five marbles are there in which all of them red or green? sets Need Help? Read Tate Tutor

Answer 1

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 :-

$C(n;r)=\dfrac{n!}{r!(n-r)!}$

Then, the number of possible sets of five marbles are there in which all of them red or green is given by :-

$C(8;5)=\dfrac{8!}{5!(8-5)!}\\\\=\dfrac{8\times7\times6\times5!}{5!3!}\\\\=\dfrac{8\times7\times6}{6}\\\\=8\times7=56$

Now, the number of possible sets of five marbles are there in which all of them red or green = 56