Question

The number of four digit odd numbers that can be formed so that no digit being repeated in any number is
A. 2240
B. 2420
C. 2440
D. 2520

Answer 1

Hint: We have to find the four-digit number. First, take the ten’s place and assume how many odd numbers can be placed in it, then go to thousands of places and assume the number of digits can be placed in it.

Complete step-by-step answer:
The number should be formed with a number of digits is 4.
It should be noted that the four digits odd number that we have to form should be less than 10000 (the last 4 digit number) and greater than 1000 ( the last 3 digit number)
Now, the four digit number consists of one’s, ten’s, hundreds and thousands digits, so the possible one’s digit will be 1, 3, 5, 7 and 9 because we have to form the odd number, so 1, 3, 5, 7and 9 are odd numbers it means one of the total 5 numbers can be placed at one’s digit.
Then the thousand’s place can be one of the 1, 2, 3, 4, 5, 6, 7, 8, and 9, but one of them is already occupied by one’s digit, then only one of the 8 numbers is possible to place in the thousand's number.
And the hundred’s also the same, 8 possible numbers, and coming to the ten’s place, we will have only 7 possible numbers to place in it.
Then the number could be \[8 \times 8 \times 7 \times 5 = 2240\]
So the number of four-digit odd numbers can be formed is 2240. It means option (A) is correct.

Note: Here, we have to know the definition of the odd number and the probability. We have to come through how a number can be formed with the help of the probability, while concluding the digit in one’s place, we have to take only odd numbers.