17. All three‐digit numbers that can be formed using the digits 1, 2, 3, 4, and 5 without
repeating the digits are
(a) 50.
(b) 60.
(c) 15.
(d) 71.
18. One of the counting rules used to determine the total number of possible outcomes for
experiments in which the order of selection does not matter or the one that ignores the
order of selection is
(a) filling the slot.
(b) k‐step experiment.
(c) permutations.
(d) combinations.
19. The number of ways of selecting k distinct objects from a group of n distinct objects
where the order of selection is important is known as
(a) number of combinations of n objects using k objects at a time
(b) number of permutations on n objects using k at a time.
(c) number of filling n slots after the first slot is filled.
(d) number of combinations of all objects in the experiment.
17. To find the number of three-digit numbers that can be formed using the digits 1, 2, 3, 4, and 5 without repeating the digits, we need to consider the following:
1. The first digit can be any of the five digits (1, 2, 3, 4, or 5). So, there are 5 options for the first digit.
2. The second digit can be chosen from the remaining four digits (since we cannot repeat digits). So, there are 4 options for the second digit.
3. Similarly, the third digit can be chosen from the remaining three digits. So, there are 3 options for the third digit.
To find the total number of options, we multiply the number of options at each step: 5 * 4 * 3 = 60.
Therefore, the correct answer is (b) 60.
18. The counting rule that is used to determine the total number of possible outcomes for experiments in which the order of selection does not matter or the one that ignores the order of selection is called "combinations."
Therefore, the correct answer is (d) combinations.
19. The number of ways of selecting k distinct objects from a group of n distinct objects where the order of selection is important is known as "number of permutations on n objects using k at a time."
Therefore, the correct answer is (b) number of permutations on n objects using k at a time.