Question

An urn contains 5 red marbles, 4 black marbles, and 3 white marbles. Then, the number of ways in which 4 marbles can be drawn so that at most three of them are red is: _________

Answer 1

To find the number of ways that 4 marbles can be drawn from the urn where at most three of them are red, we consider three different scenarios: drawing 0 red marbles, drawing 1 red marble, and drawing 2 red marbles. The total number of ways is the sum of these scenarios.

Step-by-step explanation:

To find the number of ways that 4 marbles can be drawn from the urn where at most three of them are red, we need to consider three different scenarios:

Drawing 0 red marbles: Choose 4 marbles from the 4 black and 3 white marbles, which can be done in C(7, 4) ways.

Drawing 1 red marble: Choose 1 red marble and 3 marbles from the 4 black and 3 white marbles, which can be done in C(5, 1) * C(7, 3) ways.

Drawing 2 red marbles: Choose 2 red marbles and 2 marbles from 4 black and 3 white marbles, which can be done in C(5, 2) * C(7, 2) ways.

The total number of ways to draw 4 marbles with at most three of them being red is the sum of the three scenarios.