Based off the info giving at the for exercises 29-42: A) How many sets of three

Question

Based off the info giving at the for exercises 29-42:

A) How many sets of three marbles include all the yellow ones?

B)How many sets of three marbles include none of the yellow ones?

C) How many sets of five marbles include one of each color?

Marbles For Exercises 29-42, a bag contains 3 red marbles. 2 green ones, 1 lavender one, 2 yellows, and 2 orange marbles. HINT [See Example 7] 29. How many possible sets of four marbles are there? 30. How many possible sets of three marbles are there? 31. How many sets of four marbles include all the red ones? 32. How many sets of three marbles include all the yellow ones? 33. How many sets of four marbles include none of the red ones?

Explanation / Answer

A) Total combination of 3 balls is 10C3 = 120.

if all the 2 yellow marbles are included, the other one could be one of any other colour. hence it would be the number of remaining balls i.e. 8 sets of 3 marbles would include all the yellow ones.

B) Refering to the above, 120-8 = 112 sets of 3 marbles would include NONE of the yellow ones.

C) if a set of 5 marbles include one of each colour, then there would be only one set because Lavender marble is only one in number.

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