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 n be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that all the girls stand consecutively in the queue. Let m be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that exactly four girls stand consecutively in the queue. Then the value of m/n is ?
ANSWER: 5

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

Using only the digits 2, 3 and 9, how many six digit numbers can be formed which are divisible by 6?
http://mathsvinu.blogspot.in/2015/05/indian-statistical-institute.html

Indian Statistical Institute
http://mathsvinu.blogspot.com/2015/05/combinatorics-indian-statistical.html

Counting under restriction.

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

A five digit number divisible by 3 is to be formed using the digits 0,1,2,3,4 and 5 without repetition. find the total number of ways this can be done.