An executive committee of three is selected from a group of ten. Which expression best describes the number of combinations?
These are my choices. I have to have one of these as the answer. I am stuck.
My answer was B. 10!, but I am still not sure. Can anyone help me please?
A. 10P3 (small 10 and 3)
B. 10!
C. 3P10 (small 3 and 10)
D. 10P3/3! (small 10 and 3 on top, big 3! on the bottom)
I believe you have asked this same question several times, each time under a different name
the last time it was answered for you by Damon in
http://www.jiskha.com/display.cgi?id=1301259576
This is a straightforward question dealing with
"choosing" 3 form 10, that is
C(10,3) or in your notation 10C3
10C3 is defined as
10!/(7!3!)
10P3 would be defined as 10!/7!, so in D, if we divide that further by 3! we would have the definition of 10C3
so D is the correct choice.
Sorry, I asked it twice because he didn't give me an A,B,C,D and I didn't know what he meant by the answer he gave. Thanks for answering.
To determine the correct expression that describes the number of combinations for selecting an executive committee of three from a group of ten, we can use the concept of combinations, often denoted as C(n, r) or nCr.
The formula for combinations is given by:
C(n, r) = n! / (r!(n-r)!)
In this case, we have a group of ten (n = 10) from which we need to select a committee of three (r = 3).
Let's consider each option:
A. 10P3 - This notation indicates the number of permutations of selecting 3 items from a set of 10, where ordering matters. However, for selecting a committee, the order in which executives are selected does not matter. So, this is not the correct expression for combinations.
B. 10! - This expression represents the factorial of 10, which calculates the number of permutations of all ten items. However, we are interested in combinations, which do not consider the order of selection. So, this is not the correct expression for combinations.
C. 3P10 - Similar to option A, this notation represents the number of permutations of selecting 10 items from a set of 3, which again considers ordering. Therefore, this is not the correct expression for combinations.
D. 10P3/3! - This expression involves both permutations and factorials. It represents the number of permutations of selecting 3 items from a set of 10, divided by the number of ways those 3 items can be arranged amongst themselves (3!). However, for combinations, we are only interested in the total number of ways to select the committee, regardless of order. So, this is not the correct expression for combinations.
From the options provided, the correct expression for the number of combinations of selecting an executive committee of three from a group of ten is option A:
A. 10C3 (small 10 and 3)
I hope this clarifies the correct expression for you!