How many 4 digits number which are less than 3000 can be formed from 6 digits 123456 if repetitions are not allowed?

Answer 1

Combinations of numbers

We need a 4 digit number, so I'll make 4 spaces to start, to represent our number.

__ __ __ __

For the 2nd, 3rd and 4th digits, it doesn't matter which number we choose from 123456.

Any number will work. We have 6 choices for each digit of our number.

__ _6_ _6_ _6_

For the first digit, it takes some thinking.

Our number must be less than 3000. this means the 1st digit of our number has to be a 1 or a 2. (Any number beginning with 3 will be more than 3000)

So we only have 2 choices for the 1st digit.

_2_ _6_ _6_ _6_

Now all you do is multiply your numbers together.

2 * 6 * 6 * 6 = 432 numbers, less than 3000 that you can make with the numbers 123456, having no repeats.

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The answer above assumes you allow the digits to repeat, for example it counts the number 1111.

I interpreted it to mean that you couldn't use the same digit twice in the same number.

Otherwise I don't know what "no repetitions" would mean other than the obvious "you can't use 1234 twice."

To illustrate, let's choose a simpler problem:

How many two digit numbers can you form from the digits 1 2 3 with no repeats?

The numbers are

1 2

1 3

2 1

2 3

3 1

3 2

There are six possible numbers (3 x 2), not 9 (3 x 3).

If you don't allow the same digit to be used twice, the answer to the original question is:

2 x 4 x 3 x 2

That's because you are allowed to use just two digits for the first position (1 and 2),

You have 4 digits left to go in the second position.

Once you have chosen a digit for the second position, you have 3 left to go in the third.

And then you have 2 left to go in the fourth.

Answer 2

The answer is 120.

Explanation:

Our four number digit has to be less than 3000, which tells us that the first digit has to be either 1 or 2. we have two choices for the first digit. And not to repeat we have restrict ourselves from using the number we chose for the first digit, lessening our choices. We have 5 and then 4 and then 3 for the remaining digits.

_2_ _5_ _4_ _3_

Hence: 2 * 5 * 4 * 3 = 120.

I hope this helps.😊