The number of 4 digit numbers having their digits in non-decreasing order (from left to right) constructed by using the digits belonging to the set {1, 2, 3} is ____.
(A)
12
(B)
13
(C)
14
(D)
15
Answer: (D)
Explanation:
To form a four-digit number with non-decreasing digits from the set {1, 2, 3}, we can look at the possible combinations:
1. All digits are 1s: There’s only one such number, 1111.
2. One digit is 2 and the rest are 1s: There are four such numbers, 1112, 1122, 1222, and 2222.
3. One digit is 3 and the rest are 1s: There are four such numbers, 1113, 1133, 1333, and 3333.
4. One digit is 2, one digit is 3, and the rest are 1s: There are six such numbers, 1123, 1133, 1223, 1233, 1333, and 2233.
Adding these up, we have a total of 1+4+4+6=15 four-digit numbers with non-decreasing digits from the set {1, 2, 3}.
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