Question

Compute the permutations and combinations.

How many two-digit, positive integers can be formed from the digits 1, 3, 5, and 9, if no digit is repeated?

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Answer 1

The number of two-digit, positive integers that can be formed from the digits 1, 3, 5, and 9, if no digit is repeated are: 12

Explanation:

We are asked to find the number of two-digit number that can be formed using the digits:

1,3 ,5 and 9

We know that the number of such digits possible are: 4×3=12

( Since at the first place there are 4 choices as any of the 4 numbers could come at the first place and also at the second place there are a choice of 3 numbers as the digit's can't be repeated )

Hence, the answer is: 12

Answer 2

12 integers

Explanation:

We want two-digit numbers, so let's provide two spaces:

__ __

In the first space, any of the four given numbers (1, 3, 5, and 9) can go there, so we have 4 numbers to choose from for that.

In the second space, because no digit can be repeated, we're only down to 3 possible choices. Think about it this way: if 1 was the first digit, then it can't be the second digit, so we now only have the numbers 3, 5, and 9 to put as the second digit; it's the same situation for any of the 4 numbers you put into the first digit place.

Now, multiply these two:

4 * 3 = 12

There are 12 such numbers.