Question

A doctor has 5 doses of flu protection vaccine left. he has 6 women and 10 men who want the medication. if the names of 5 of these people are selected at​ random, determine the probability that 5 ​men's names are selected. the problem is to be done without replacement. use combinations to determine the probability. question content area bottom part 1 the probability is enter your response here. ​(type an integer or a simplified​ fraction.)

Answer 1

To calculate the probability of selecting 5 men's names out of 6 women and 10 men without replacement, we use combinations. The probability is calculated as C(10, 5) divided by C(16, 5) resulting in a fraction of 63/1092.

Step-by-step explanation:

To determine the probability that 5 men's names are selected out of a total of 6 women and 10 men, we use combinations. We have 16 people total, and we need to choose 5 without replacement.

First, we calculate the total number of ways to choose 5 people from 16, which is given by the combination formula C(n, k) = n! / (k!(n - k)!). So, C(16, 5) calculates all the possible groups of 5 people that can be chosen. Next, we calculate the number of ways to choose 5 men from the 10 men available, which is C(10, 5).

The probability is the number of ways to choose 5 men divided by the total number of ways to choose 5 people, so:

Probability = C(10, 5) / C(16, 5).

Calculating both combinations, we get:

• C(10, 5) = 10! / (5!(10 - 5)!) = 252
• C(16, 5) = 16! / (5!(16 - 5)!) = 4368

So the probability = 252 / 4368 = 63/1092, which is the simplified fraction.