BrentGMATPrepNow wrote:
Bunuel wrote:
A student committee on academic integrity has 90 ways to select a president and vice president from a group of candidates. The same person cannot be both president and vice president. How many candidates are there?
A. 7
B. 8
C. 9
D. 10
E. 11
Let t = TOTAL number of candidates
So....
# of ways to select a president = x
# of ways to select a vice-president = x - 1
Total number of ways to select both = (x)(x - 1)
We're told that 90 ways are possible
So, (x)(x - 1) = 90
Expand: x² - x = 90
Rearrange: x² - x - 90 = 0
Factor: (x - 10)(x + 9) = 0
So, x = 10 OR x = -9
Since x cannot be negative, it must be the case that x = 10
Answer: D
Cheers,
Brent
Hi Brent, in the solution above, you basically applied Slot method to solve the problem. As far as I know, in the Slot Method, the order is considered i.e. the following two cases are counted as separate
CASE 1: President is selected first, Vice-President is selected next
CASE 2: Vice-President is selected first, President is selected next
However, I do not understand here why the order of selection shall be considered since this problem is similar to selecting a team of two people from a group of people (For e.g. Selecting a team of 2 people from a group of 6 people can be done in C(6,2) = 6!/2! 4! = 15 ways ). Could you please enlighten me on this.