Question

Find how many numbers greater than 400,000 can be made using all the digits of 416566​

Answer 1

To find the number of numbers greater than 400,000 that can be made using all the digits of 416566, arrange the digits in (6-1)! = 5! = 120 ways.

Step-by-step explanation:

To find how many numbers greater than 400,000 can be made using all the digits of 416566, we need to determine the number of arrangements of these digits that are greater than 400,000. The first digit must be 4, as it needs to be greater than 4 in order for the entire number to be greater than 400,000. The remaining digits can be arranged in (6-1)! = 5! = 120 ways. Therefore, there are 120 numbers greater than 400,000 that can be made using all the digits of 416566.

Answer 2

20

Step-by-step explanation:

You have to fill in 6 slots _ _ _ _ _ _.

Since first digit must be 4, there is only 1 way to fill in the 1st slot.

with the 5 slots, we fill in the 6s first, 3 of them.

So we have 5 options and 3 items to fill, (5 choose 3).

Then 2 ways to fill 1 and 1 way to fill 5. (It doesn't matter if you pick 5 or 1 first).

So it becomes (5C3) * (2C1) *(1C1)

= 1 * 5!/(3!)(5-3)! * (2) * 1

= 20