Question

A number of four different digits are formed by using the digits 1, 2, 3, 4, 5, 6, 7 in all possible ways without repetition.

How many of them are greater than 3400

Answer 1

How many total possible numbers can you make? 7 digits available, and you're choosing 4. Order matters, since 1234 is different from 4321.

Total possible 4-digit numbers = \({}_7P_4=\dfrac{7!}{(7-4)!}=840\)

How many of these are greater than 3400?

Answer 2

i have another question

Answer 3

You still haven't answered mine, though. How many of the 840 possible are greater than 3400?

Answer 4

u answered as 840 right?

Answer 5

No, that's the *total* possible 4-digit numbers. Some of those are less than 3400.

Answer 6

that i dont know

Answer 7

The smallest number you can come up with is 34XX. Here, you have 5 remaining possibilities for the third digit and 4 for the fourth = 20 possible permutations.

Suppose the first digit isn't a 3; this means you have 4 possibilities for the first digit, 6 for the second, 5 for the third, and 4 for the fourth = 480 possibilities.

So the total would be 500, unless there's gap somewhere in my reasoning.

Answer 8

another way :-
numbers greater than 3400 = total permutations - numbers less than 3400
= 7p4 - 2*6p3 - 2*5p2

Answer 9

http://www.wolframalpha.com/input/?i=%287+permute+4%29+-+2*%286+permute+3%29+-+2*%285+permute+2%29

Answer 10

how many exactly divisible by 2,4,25

Answer 11

for a number to be divisible by 2,
its unit digit has to be even i think

so just see how many permutations have the units digit as even : 2, 4, 6