Permutations & Combinations Questions (855)

Number of 5-digit natural numbers such that product of their digits equals number of ways to create a necklace out of 6 beads from 10 distinct beads is

The number of 5-digit numbers in non-decreasing order that can be formed using digits \(0, 1, 2, \ldots, 7\) (with repetition allowed) such that the number starts with 1 is (from the table, number starting with 1 uses digits 1, 0): What is the 2005th such number (5-digit numbers written in non-increasing order of digits from digits \(0\) to \(9\))?

The number of natural numbers less than 7,000 which can be formed by using the digits 0, 1, 3, 7, 9 (repetition of digits allowed) is equal to __________.

The number of natural numbers lying strictly between 212 and 999 with digit sum equal to 15 is

\(10^n + 3(4^n + 2) + 5\) is divisible by (n ∈ ℕ)