Question

The digits 0-9(0,1,2,3,4,5,6,7,8,9) can be rearranged into 3628800 distinct 10 digits numbers.

How many of these numbers are prime. ​

Answer 1

Answer:

there are 2 prime nos in them

3 and 2

Step-by-step explanation:

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Answer 2

No such number is prime.

Given: Digits 0-9 arranged into distinct 10-digit arrangements

To find: How many numbers are prime

Solution:

We are given that,

0-9 digits are arranged into distinct 10-digit numbers.

⇒ every arrangement has all digits from 0 to 9

⇒ sum of digits of every number = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9

⇒ sum of digits = 45

We know that 45 is divisible by 3

⇒ By the divisibility rule of 3,

every given 10-digit number is divisible by 3

⇒ 3 is a factor of all such numbers

⇒ No such number is prime.

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