Question

17.
(
Show that there are 4536 numbers between
1000 and 10000, which have none of their digits
repeated. Of these, how many are odd numbers ?​

Answer 1

Answer:

hahNJIKANABAH qiiavavav6992

Answer 2

The number of odd numbers is 2268 .

Explanation:

Digits between 1000 and 10000, are

1001, 1002,...............9999.

i.e. all digits are four-digits number .

According to Permutations , the number of 4-digit numbers which have none of their digits  repeated= $9\times9\times8\times7$  [The number of choice of first place is 9 (0 is not included), the number of choices for 2nd place is also 9 0 is included),  the number of choices for 3rd place is 8 ,  the number of choices for 4th place is 7]

Thus , the number of 4-digit numbers which have none of their digits  repeated= 4536

Hence , proved.

Since there are equal number of odd and even numbers , thus the number of odd numbers= $\dfrac{4536}{2}=2268$

# Learn more :

How many natural numbers are there between 1 to 1000 which have none of their digits repeated?

https://brainly.in/question/2752608