a committee of 5 people is to be selected from a group of 6 men and 9 women. If the selection is made randomly, what is the probability that the committee consists of 3 men and 2 women?
Prob = C(6,3)*C(9,2)/C(15,5) = 20*36/3003 = 240/1001
0.23976
To find the probability of selecting a committee with 3 men and 2 women, we need to calculate the total number of ways we can form a committee with these specifications and divide it by the total number of possible committees.
Let's break it down step by step:
Step 1: Calculate the total number of ways to select a committee of 5 people from the group of 6 men and 9 women. This can be done using the combination formula:
C(n, r) = n! / (r! * (n-r)!)
In this case, n = 15 (6 men + 9 women) and r = 5 (5 people in the committee).
C(15, 5) = 15! / (5! * (15-5)!) = 3003
So, there are 3003 possible committees that can be formed from the group.
Step 2: Calculate the number of ways to select 3 men and 2 women from the group.
The number of ways to select 3 men from the 6 available men is C(6, 3) = 6! / (3! * (6-3)!) = 20.
Similarly, the number of ways to select 2 women from the 9 available women is C(9, 2) = 9! / (2! * (9-2)!) = 36.
Step 3: Multiply the number of ways to select 3 men and 2 women together:
20 * 36 = 720.
Step 4: Divide the number of ways to select 3 men and 2 women by the total number of possible committees:
720 / 3003 = 0.2398 (rounded to four decimal places).
Therefore, the probability of selecting a committee consisting of 3 men and 2 women is approximately 0.2398 or 23.98%.
To find the probability of selecting a committee of 3 men and 2 women, we need to find the total number of ways to select 5 people from a group of 6 men and 9 women, and divide it by the total number of possible selections.
First, let's find the total number of ways to select 5 people from the group of 6 men and 9 women. This can be calculated using combinations.
The number of ways to choose 3 men from 6 is given by the combination formula: C(6, 3) = 6! / (3!(6-3)!) = 20.
The number of ways to choose 2 women from 9 is given by the combination formula: C(9, 2) = 9! / (2!(9-2)!) = 36.
Since we want to choose 3 men and 2 women, we need to multiply the number of ways to choose men by the number of ways to choose women: 20 * 36 = 720.
Now, let's find the total number of possible selections. We need to choose 5 people from a group of 6 men and 9 women, which can be calculated using combinations.
The total number of ways to choose 5 people from the 15 available individuals is given by the combination formula: C(15, 5) = 15! / (5!(15-5)!) = 3003.
Therefore, the probability of selecting a committee consisting of 3 men and 2 women is:
P(3 men and 2 women) = number of ways to choose 3 men and 2 women / total number of possible selections = 720 / 3003 ≈ 0.2398.
So, the probability is approximately 0.2398, or 23.98%.