8 students have been chosen to play for PCU's inter-collegiate basketball team. If every person on the team has an equal chance of starting, what is the probability that both TOM and Alex will start?
(Assume 5 starting positions)
Of the 8 students, 5 will be starters, 3 will be non-starters.
Tom and Alex will both be starters if neither is selected to be a non-starter.
P(1st non-starter is not Tom or Alex) = 6/8. (Of the 8 students, there are 6 besides Tom and Alex.)
P(2nd non-starter is not Tom or Alex) = 5/7. (Of the 7 remaining students, there are 5 besides Tom and Alex.)
P(3rd non-starter is not Tom or Alex) = 4/6. (Of the 6 remaining students, there are 4 besides Tom and Alex.)
Since we want all 3 events to happen, we multiply the fractions:
6/8 * 5/7 * 4/6 = 5/14.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
