5 Questions...

[proff.hacker]

could you help me to find the solution of the following questions:

1- How many strings of 20 decimal digits are there that contain two 0s, four 1s, three 2s, one 3, two 4s, three 5s, two 7s, and three 9s?

2- How many solutions are there to the inquality:
x1 + x2 + x3 £ 11
Where x1, x2, and x3 are nonnegative integers? (Hint: Introduce an auxiliary variable x4 so that x1 + x2 + x3 +x4 = 11.)

3- How many positive integers less than 1,000,000 have exactly one digit equal to 9 and have a sum of digits equal to 13?

4- How many ways are there to distribute five distinguishable objects into three indistinguishable boxes?

5- How many terms are there in the expansion of (x + y + z)^ 100?


thanks and regards