Question Detail

STA 112 PERMUTATIONS AND COMBINATIONS Objective Question

Question

There are 6 letters and 3 post boxes. The number of ways in which these letters can be posted is:
Options
A 6<sup>3</sup>
B 3<sup>6</sup>
Correct Answer
C <sup>6</sup>P<sub>3</sub>
D <sup>6</sup>C<sub>3</sub>
Correct Answer

Option B is the correct answer.

Detailed Explanation

Each of the 6 letters can be posted into any one of the 3 post boxes. The choice for one letter is independent of the choices for other letters.For the first letter, there are 3 choices of post boxes.For the second letter, there are 3 choices of post boxes....For the sixth letter, there are 3 choices of post boxes.By the multiplication principle, the total number of ways is 3 × 3 × 3 × 3 × 3 × 3 = 36.

Hint

Consider the choices for each item (letter) independently and how many options are available for each choice (post boxes).

Question Info