Question

A bag contains 8 red balls and 5 blue balls. In how many ways can 3 red balls and 4 blue balls be drawn from the bag?

A) 1540
B) 336
C) 280
D) 420

Answer 1

To draw 3 red balls and 4 blue balls from the given bag, we can use combinations to find the number of ways. The total number of ways is found by multiplying the number of ways to choose each color. Therefore, the correct answer is C.

Step-by-step explanation:

To find the number of ways to draw 3 red balls and 4 blue balls from a bag containing 8 red balls and 5 blue balls, we can use combinations.

The number of ways to choose 3 red balls from 8 is given by C(8, 3) = 8! / (3!(8-3)!) = 8! / (3!5!) = 56.

The number of ways to choose 4 blue balls from 5 is given by C(5, 4) = 5! / (4!(5-4)!) = 5! / (4!1!) = 5.

Since these two events are independent, we can multiply the number of ways for each event to get the total number of ways to draw 3 red balls and 4 blue balls. Therefore, the answer is 56 * 5 = 280.

So, the correct option is C) 280. Now, we multiply the number of ways to choose the red balls by the number of ways to choose the blue balls:

Number of ways = C(8,3) × C(5,4)

Number of ways = 56 × 5

Number of ways = 280

The correct answer is C) 280.