GATE CS 2015 Set 3 — Question 25
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Engineering Mathematics → Sets & Combinatorics → Permutations & Combinations
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Question
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 is __________.
Correct answer
15 to 15
Solution
We need to form a 4-digit number such that using digits from the set .
This is a problem of combinations with repetition (stars and bars), as the order is fixed (non-decreasing) and determined solely by the count of each digit chosen.The number of ways to choose digits from types with repetition is given by:Alternatively, we can list the combinations:
This is a problem of combinations with repetition (stars and bars), as the order is fixed (non-decreasing) and determined solely by the count of each digit chosen.The number of ways to choose digits from types with repetition is given by:Alternatively, we can list the combinations:
- All same (e.g., 1111): 3 ways
- 3 same, 1 different (e.g., 1112): ways
- 2 same, 2 same (e.g., 1122): 3 ways
- 2 same, 2 different (e.g., 1123): 3 ways
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