Combinatorics

Find the sum of all distinct four digit numbers that can be formed
using the digits 1, 2, 3, 4, 5, each digit appearing at most once.

Determine the number of 3-digit numbers in base 10 having at least one 5 and at most one 3.
Ans: 249

Find the sum of all 3-digit natural numbers which contain at least one odd digit and at least one even digit.
Ans: 370775

Let S={(a1,a2,a3)}| 0≤ ai ≤ 9 and a1+a2+a3 isdivisibleby3}. Find the number of elements in S.

The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices (0,0), (0,41) and (41,0), is:
1) 861
2) 820
3) 780
4) 901