Help to figure it without writing it .?

Question

How many ways can you arrange the numbers 5,3,2 and 3 to form different 4-digit nos ,using each number exactly once,where the number is greater than 3000?

Answer 1

I'm afraid that MamaMia has double-counted, by treating each of the " 3's " as INDEPENDENT, DIFFERENT digits. They're NOT! They're indistinguishable when they are interchanged within any given number. You actually asked for all of the DIFFERENT 4-digit numbers. For example, if 3_1 is "3 number 1" and 3_2 is "3 number 2" :

The number 5 2 (3_1) (3_2) is the SAME as 5 2 (3_2) (3_1).

Therefore, the answer is :

THE NUMBERS CAN BE ARRANGED IN 9 WAYS.

The requirement to "not write it" ("it" being "helping to figure it") seems unduly restrictive, and indeed quite inconsistent with this Yahoo! Answers service :

HOW DO YOU EXPECT TO SEE AN ANSWER, IF IT'S NOT WRITTEN ??!! WILL YOU EMPLOY TELEPATHY?

So, with SOME (minimal?) writing, here's how to do it :

The numbers must begin with 3 or 5. Take numbers of the form 3xxx first, then deal with types 5yyy:

(i) Case 3xxx : the remaining 2, 3 and 5 may be arranged in 6 ways. (Choose the first one in three ways, then the second in two ways, and that's it.)

(ii) Case 5yyy : the remaining 2, 3, 3 can only be arranged in 3 DIFFERENT ways; all that matters is whether the " 2 " goes in the first, second or third of the remaining places ; in each case the other two digits are necessarily " 3."

So the number of ways [from cases of type (i) and (ii)] is 6 + 3 = 9.

Live long and prosper.

Answer 2

The first digit can be a 5 or a 3.

If 3 then then:
2nd digit can be 2,3, or 5
3rd is one of the remaining 2
4 is the remaining number

or 3 * 2 = 6

When 5 is the first number
If the 2nd number is 3 then
third can be 2 or 3

2 * 1 = 2

When 5 is the first
and 2 is the 2nd
3 will be the third and 4

1

I would say the answer is 9

Answer 3

It's a four digit number > 3000.

The first number can be any of 3 digits (5,3, or 3). Two cannot be the first digit, or the number will not be > 3000.

The second number can be any of the three remaining digits not used in the first placeholder.

The third, any of the two remaining unused digits.
The fourth must be the one remaining unused digit.

Ways to arrange = (3)(3)(2)(1) = 18

Answer 4

It helps to write it but you just have to look at the fact that one number (2) cannot be used at be greater than 3000 if it is the first digit . you then have to know how many combos can be made and plug them into a mathematical equation to get the result. anyway you slice it you are going to need a piece of paper.