BTGmoderatorLU wrote: ↑

Fri Jul 31, 2020 11:23 am

Source: Magoosh

An equal number of juniors and seniors are trying out for six spots on the university debating team. If the team must consist of at least four seniors, then how many different possible debating teams can result if five juniors try out?

A. 50
B. 55
C. 75
D. 100
E. 250

The OA is B

If the team must have AT LEAST 4 seniors, then we must consider two possible cases:
Case i: The team has 4 seniors and 2 juniors
Case ii: The team has 5 seniors and 1 junior

Case i: The team has 4 seniors and 2 juniors
Since the order in which we select the seniors does not matter, we can use combinations.
STAGE 1: We can select 4 seniors from 5 seniors in 5C4 ways (= 5 ways)
STAGE 2: We can select 2 juniors from 5 juniors in 5C2 ways (= 10 ways)
By the Fundamental Counting Principle (FCP), we can complete both stages in (5)(10) ways = 50 ways

Aside: See the video below to learn how to quickly calculate combinations (like 5C2) in your head

Case ii: The team has 5 seniors and 1 junior
STAGE 1: We can select 5 seniors from 5 seniors in 5C5 ways (= 1 way)
STAGE 2: We can select 1 junior from 5 juniors in 5C1 ways (= 5 ways)
By the Fundamental Counting Principle (FCP), we can complete both stages in (1)(5) ways = 5 ways

TOTAL number of outcomes = 50 + 5 = 55

Answer: B

Cheers,
Brent

VIDEO ON CALCULATING COMBINATION IN YOUR HEAD
https://www.gmatprepnow.com/module/gmat ... /video/789