Question

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 1

Answer: 35

Explanation:

Given : A bag contains four red marbles, two green ones, one lavender one, three yellows, and one orange marble.

Total = 4+2+1+3+1=11

To find sets of four marbles include none of the red ones, we need to exclude red marbles when we count the total number of marbles.

Then, the total marbles(exclude red) =11-4=7

Now, the combination of 7 marbles taking 4 at a time is given by :-

`^7C_4=(7!)/(4!(7-4)!)=(7*6*5*4!)/(4!3!)=35`

Hence, the number of sets of four marbles include none of the red ones = 35