an executive committee of three is selected from a group of ten which expression best describes the number of combinations?
A)10P3
B)10!
C)D)10P3/31
The expression that best describes the number of combinations for selecting an executive committee of three from a group of ten is A) 10P3.
To understand why, we need to understand what each expression represents:
A) 10P3 represents the number of permutations of selecting 3 people from a group of 10. In other words, it calculates the number of ordered arrangements where the order matters.
B) 10! represents the factorial of 10. In general, n! (read as "n factorial") represents the product of all positive integers from 1 to n.
C) D) are not valid options as they are not conventional mathematical expressions for counting combinations.
In this case, we are interested in the number of combinations where the order does not matter. When selecting a committee, the order in which the members are chosen does not affect the outcome. Therefore, we need to use the combination formula.
The combination formula for selecting r items from a set of n items is represented as nC_r (read as "n choose r") and is calculated as:
nC_r = n! / (r! * (n-r)!)
In our case, selecting an executive committee of 3 from a group of 10, the expression is:
10C3 = 10! / (3! * (10-3)!) = 10P3
Therefore, the correct expression that best describes the number of combinations is A) 10P3.