can someone correct this problem for me thanks
A group of 7 workers decide to send a delegation fo 2 to their superviosr to discuss their grievances.
a) how many delegations are possible?
my answer: 21
b)If it is decided that a particular worker must be in the delegation, how many different delegations are possible?
my answer: 6
c) I fhtere is 2 women and 5 men in the group, how many delegations would include at least 1 women?
my answer: 11
a is not correct.
b is correct
On c, you can figure the number of delegations that have no women, then subtract that from the correct answer in a.
The number of ways to have no women is 5*4.
a) 7*6*5*4*3*2*1/5*4*3*2*1=7*6=42 possiilites
b) 1*6=6 possible combinations
c) 22 possibilites
To correctly answer the questions, let's break down each scenario:
a) How many delegations are possible?
In this case, we are selecting 2 members from a group of 7 workers. This can be represented as "7 choose 2," denoted as 7C2. The formula to calculate this is nCr = n! / (r!(n-r)!), where n is the total number of items and r is the number of items being selected. Applying the formula, we have 7C2 = 7! / (2! * (7-2)!), which simplifies to 7! / (2! * 5!). Evaluating this expression, we get 7! = 7 * 6 * 5!, which cancels out the 5! terms, leaving us with (7 * 6) / (2 * 1). This simplifies further to 42 / 2, resulting in 21. Therefore, the correct answer is 21.
b) If a particular worker must be in the delegation, how many different delegations are possible?
In this case, we are fixing one worker and selecting the other member from the remaining 6 workers. Thus, we have 6 possible choices for the second member. Therefore, the correct answer is 6.
c) How many delegations would include at least 1 woman?
To determine the number of delegations with at least 1 woman, we first need to find the total number of possible delegations without any women. Since there are 5 men, we need to choose 2 men from this group. This can be represented as "5 choose 2," or 5C2, which we can calculate similarly to the previous question: 5C2 = 5! / (2! * (5-2)!), which simplifies to (5 * 4) / (2 * 1) = 10.
Next, we subtract the number of possible delegations without any women from the total number of delegations calculated in part a. So the correct answer for part c is 21 (total delegations from part a) - 10 (delegations without any women) = 11.
In summary:
a) The correct number of possible delegations is 21.
b) The correct number of delegations with a fixed worker is 6.
c) The correct number of delegations with at least 1 woman is 11.