Question

How many 4-digit numbers divisible by 5, all of the digits of which are odd, are there

Answer 1

So we must create 4-digit numbers with the 5 odd digits in the image.

First, a number is only divisible by 5 if the last digit is 0 or 5, and we only can use the last digit equal to 5 (because 0 is not in the image).

if each odd number can be used only once, we have:

Now, for the other 3 digits we have 4 options.

So for the first one we have 4 options,

for the second we have 3 options (because one is already taken)

for the last one we have only 2 options

then the number of combinations is:

C = 4*3*2 = 24.

If the numbers can be repeated (for example, 5555 is allowed, then)

we still have our last digit fixed in 5, and for the first digit we have 5 options, for the second we also have 5 options, and for the third we also have 5 options, then we have a total of:

C = 5*5*5 = 25*5 = 125 combinations.