Question

Assume that there are 8 rats in the cage: 6 trained and 2 untrained. A rat is removed from the cage and it is noted whether or not it is trained. It is then placed in a different cage. 4 more rats are removed and treated the same way. How many outcomes are possible for this experiment?
(1) Which of the following is not a valid outcome for this experiment?
A. UUTTU
B. UTTUT
C. TUTTT
(2) How many outcomes are possible for this experiment?

Answer 1

Answer:

1. Option A

2. 56

Explanation:

1.

Option A

Option A is not a valid answer for this question as it is given that out of eight rats only two rats are untrained. Thus, an output which shows more that two untrained rats i.s UUTTU is a wrong answer

2.

$8C_5 = \frac{8!}{5!(8-5)!} \\8C_5 = \frac{8*7*6*5!}{5! * 3!} \\8C_5 = \frac{8*7*6}{3*2*1} \\8C_5 = 56$

Thus , there are 56 outcomes possible for this experiment