1.A group of five people consists of two women.Alice,Betty, and three men, Carl,David and Ed. Find the number of ways in which this can be done if the chairperson and treasurer are both men.
I used here permutation.How can I find in such question I can use permutation.
There are 3P2 = 6 ways to pick the chairman and treasurer.
If the other three positions are also specific, then there are 3! ways to seat them, as well. You're kind of unclear on just how the group is to be formed.
google is always a good resource when searching for general examples and discussions.
In this question, you need to find the number of ways to arrange the five people in a group, given that the chairperson and treasurer positions are reserved for men. Since there are three men in the group, you need to find the number of permutations of arranging 3 men and 2 women.
To solve this using permutation, you can follow these steps:
Step 1: Determine the total number of people. In this case, there are two women (Alice and Betty) and three men (Carl, David, and Ed), giving a total of 5 people.
Step 2: Identify the number of positions to be filled. In this case, there are two positions: chairperson and treasurer.
Step 3: Identify the number of men available to fill each position. Since both the chairperson and treasurer must be men, you have three men (Carl, David, and Ed) available for each position.
Step 4: Calculate the number of permutations. We can use the permutation formula to calculate the number of ways to arrange the three men for the chairperson position and the treasurer position. The permutation formula is given by P(n, r) = n! / (n - r)!, where n is the total number of objects and r is the number of objects being arranged.
Calculating the number of ways to arrange the three men (3!) for the chairperson position, we have:
P(3, 1) = 3! / (3 - 1)! = 3
Calculating the number of ways to arrange the three men (3!) for the treasurer position, we have:
P(3, 1) = 3! / (3 - 1)! = 3
Step 5: Multiply the two permutations calculated in step 4. Since the positions are independent of each other, we can multiply the number of ways to arrange the chairperson and treasurer to find the total number of arrangements.
So, the total number of ways to arrange the group with the chairperson and treasurer positions filled by men would be 3 * 3 = 9.
Therefore, in this case, using permutation, you can determine that there are 9 ways to arrange the group of five people with two women (Alice and Betty) and three men (Carl, David, and Ed) if the chairperson and treasurer positions are both men.