math problemsss..

Question

1.A store has four open checkout stands. In how many ways could six customers line up at the checkout stands?

2.Let N be the smallest number divisible by 33 which is greater than 1,000,000 and whose digits are all 0's and 1's. What are N's leading four digits?

3.In how many ways can slashes be placed among the numbers 123456789 to separate then into four grops with each group including at least one letter?

if you know any of the above questions, please help me..
thanks~^^

if possible, please show your steps as well~^^

Answer 1

Q2.

N=1101111

where N%33==0 && N>1000000

So the four leading digits are 1101.

Answer 2

1.

Each customer has 4 choices of checkout stand

Therefore no. of ways of 6 customer lining up at the checkout stands

= 4^6

= 4096


2.
Sorry, don't know the meaning of 0' , 1' and N'

3.
There are 8 locations where slash can be placed.
To separate into 4 groups, 3 slashes are required.
Therefore, no. of ways
= 8C4
= (8x7x6x5)/(4x3x2x1)
= 70

Answer 3

1. 6*4^6 = 24,576 ways

2. Sorry no idea on the question

3. There are 8 spaces between 123456789 so to insert 4 splits, the possible ways are
= 8C4
= 70

Answer 4

1.24
2. 30
3.54


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