Question

In Jim's cooler there are 9 bottles of soda and 7 bottles of water. Jim is going to choose 10 bottles at random from the cooler to give to his friends. What is the probability that he will choose 6 sodas and 4 waters?

Answer 1

To calculate the probability, we can use the concept of combinations. The probability that Jim will choose 6 sodas and 4 waters from the cooler can be calculated using the formula for combinations.

Step-by-step explanation:

In this problem, we can use the concept of combinations to solve for the probability. The total number of bottles in the cooler is 9 sodas + 7 waters = 16.

Jim is choosing 10 bottles at random, so the total number of possible outcomes is C(16, 10).

Now, we need to calculate the number of ways Jim can choose 6 sodas and 4 waters.

There are C(9, 6) ways to choose 6 sodas from the 9 available, and C(7, 4) ways to choose 4 waters from the 7 available.

Therefore, the probability that Jim will choose 6 sodas and 4 waters is:

P(6 sodas and 4 waters) = C(9, 6) * C(7, 4) / C(16, 10)