Question

Write a- 6 digit number using all the digits 2,3,4,5,1,7 only once
1) Which is divisible by 4.
2) Which is divisible by 5.​

Answer 1

Answer:

There are 6!=720 six digit numbers made up of the given digits.

Among them, how many are multiple of 4? Okay, just notice that a six digits number is divisible by 4 if the number formed by its two last digits is divisible by 4.

For example, consider 324156 . We have 324156=3241⋅100+56 . Since 100 is divisible by 4, you only need to check 56 .

Now, how many 2 digits numbers divisible by 4 can be formed with one of {1,2,3,4,5,6} without repetition? The last digit is obviously one of {2,4,6} . So it is easy to see that {12,32,52,24,64,16,36,56} are these numbers. So we now know the 8 couples of last digits that will make six digits numbers be divisible by 4.

There are 4! permutations for the first 4 digits. So, there are 8⋅4! six digits numbers divisible by 4.

Your probability is thus p=8⋅4!6! .

Hence p=415 .

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Answer 2

Step-by-step explanation:

0,5 divisible by in 5

the rule for 4:a number is divisible by 4 if it's last two digits are evenly divisible by 4. For example,2312. The last two digits are 12 and it is divisible by 4