Question

Two-digit natural numbers are formed, with replacement, from the digits 0 through 9.

Answer 1

Answer:

The first digit of a two digit number can be any of digits 1 - 9. It cannot be 0 though. Therefore there are 9 possible digits for the first place.

There are 5 possible digits for the second position. The two digit number has to be odd and therefore the final digit must be 1,3,5,7 or 9

Therefore for each and every one of the nine first digits there are 5 digits that the second can be.

Therefore ANSWER = 9 * 5 = 45 possible permutations.

2. The largest two digit number = 99

Subtract 57 and you get 42

ANSWER = 42

The forty two numbers are 58 ,59, 60, 61......98, 99

Answer 2

Answer:

50 two-digit odd numbers are formed

Step-by-step explanation:

From the digits from 0 to 9 to get two -digit odd numbers you will need to pair numbers from

0 to 9 as the first digit of the numbers = 10 possible numbers

and also you will need to pair the first digits with an odd number as the second digit .

to get the odd numbers as second digits you will need to pick from

 1 , 3 , 5 ,7 and 9 = 5 possible numbers.

zero is  considered in the first digit because zero can start a two digit natural number and zero is not considered in the second digit because zero is an even number.

to get the possible two -digit number you will have to multiple the possible numbers for the first digits with the possible numbers for the second digits which is =

        10 * 5 = 50 hence there will be 50 possible two-digit  odd numbers.