Counting
When (a+b+c+d)10 is expanded and like terms combined, how many terms are in the result?
13c3
How many ordered pairs of integers (a, b, c) between 1 and 7 are such that abc is a multiple of 7?
Anna the anteater is standing at the bottom-left corner of a 6 x 6 grid and wants to reach the top-right corner. On each move, she can either go one unit up or one unit to the right. Unfortunately, before she begins moving, an asteroid hits the grid, and causes a 2 x 2 sized hole to be formed at the top-left corner of the grid (this means she can't travel in or around the hole). How many ways are there for her to reach her destination?
662
The base 6 number 15a4b_6 is divisible by 7. What is the sum of all possible values of a+b?
9
Anna, Laura, Iris, Banna, Baura, and Biris are standing in a line. Anna is in front of Laura, Laura is in front of Iris, Banna is in front of Baura, and Baura is in front of Biris. In how many ways can they line up?
In how many ways can 3 Americans, 4 Germans, 2 Frenchmen, and 3 Russians sit around a circular table if those of the same country sit together?
10368
In the figure below, a move from point number A to point number B can only occur if B > A and the two points are in the same row or column. Find the total number of ways to go from point 1 to point 30.
671
How many ordered triples (a, b, c) are there such that a,b, and c are primes and abc = 11(a + b + c)?
12
Peanut, Kitkat, Anna, Grace, and a mouse are to be seated in a row of twenty chairs. If no two things can sit next to each other, how many ways can they be seated?
16c5
How many nonnegative integer solutions are there to the equation x1 + x2 + x3 <= 50?
53c3
Jack starts at one corner of a tetrahedron. In a move, he walks along one edge to a different corner. In how many ways can he end up on the same edge again after 6 moves?
183
What is the coefficient of x10 in the polynomial (1+x+x2+...+x10)(1+x)10?
1024