Answer:
Step-by-step explanation:
Exactly two numbers appear:
There are
(
6
2
)
(62)
ways for two of the six numbers to appear. On each of the six rolls of the die, there are two possible outcomes, giving
(
6
2
)⋅
2
6
(62)⋅26
possible outcomes in which two of the six numbers appear. However, of these
2
6
26
sequences, there are two in which the same number is rolled six times. Thus, the probability of exactly two numbers appearing in six rolls of the die is
(
6
2
)⋅(
2
6
−2)
6
6
