Permutations & Combinations
5-digit Numbers Greater than 40000, Divisible by 5
nta_pyq_2023_apr
Grade 11
Question:
5-digit numbers $>40000$, divisible by 5, from $\{0,1,3,5,7,9\}$ without repetition is equal to
Step-by-Step Solution
Key Concept: First digit $\geq4$: possible $\{5,7,9\}$ (4 excluded since $>40000$, and if first $=4$... no 4 in set). Actually $>40000$ with digits from set: first digit $\in\{5,7,9\}$ OR first $=4$? 4 not in set. First digit $\in\{5,7,9\}$. Last digit $\in\{0,5\}$ for div by 5.
120 numbers.
Correct Answer: 2