A bag contains 3 red marbles 3 green ones 1 lavender one 2 y

A bag contains 3 red marbles, 3 green ones, 1 lavender one, 2 yellows, and 2 orange marbles.

How many sets of five marbles include at least two red ones?

Solution

Total marbles = 11

5 marbles are selected

Atleast 2 must be red.

Hence (2 r, 3 others) or (3 r, 2 others) should be selected.

No of ways = 3C2(8C3)+(3C3)(8C2)

= 3(56)+28

=196

Hence 196 sets of five marbles include at least two red ones