If a problem is solved. It is not 'the' answer.
No attempt is made to search for the most elegant answer.
I highly recommend that you at least try to solve the
problem before you read the solution.
In how many ways can you stack 7 different books, so that a specific book B is on the third place? 
In how many ways can you take 3 marbles out of a box with 15 different marbles? 
In a firm are 20 workmen and 10 employees. In how many ways can you construct a delegation with 3 workmen and 2 employees? 
In how many ways can you take 5 cards, with at least 2 aces, out of a game of 52 cards? 
In how many ways can you split a group of 13 persons in 3 persons and 10 persons? 
How many diagonals are there in a convex npolygon? 
How many numbers consisting of 3 digits, can you make with the digits 0,1,2,3,4 ? 
How many subsets are there in a set S of 10 elements? 
Calculate the term with x^{2} in the expansion of (x^{3} + 1/2x)^{10} 
1011011101 is an example op a binary number of length 10. How many binary numbers of length 10 end up with 111 and contain exactly two zeros. 
In how many ways can you stack m identical bricks into k boxes
so that each box contains at least 1 brick. 
From a deck of cards we take 12 cards.

How many strictly positive integer solutions ( x, y , z) are there, such that x + y + z = 100 
How many terms are contained in (a + b + c)^{20} . 
The term A.a^{10} b^{3} c^{7} is present in the development of (a + b + c)^{20}
Calculate A. 