Question

A bag contains three red marbles, two green ones, one lavender one, two yellows, and two orange marbles. HINT [See Example 7.] How many sets of seven marbles include at least one yellow one but no green ones

Answer 1

Answer: 8

Explanation:

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

Total marbles other than green = 8

Total marbles other than green and yellow = 6

Then the number of sets of seven marbles include at least one yellow one but no green ones:-

`^(2)C_1*^(6)C_6+ ^2C_2*^6C_5\\\\= 2* 1+1*6\\\\=2+6=8`

Number of sets of seven marbles include at least one yellow one but no green ones = 8