Question

I am thinking of a four digit number. The sum of the four digits is 6, but none of the digits is zero. If you have only one opportunity to guess the number, what is the probability that your guess is correct?

Answer 1

Obviously, digits must be allowed to repeat, otherwise
the smallest combination would be 1234, and that sum is 10
So allowable choices:
1113 ---> arrange in 4!/3! or 4 ways
1122 ---> arrange in 4!/(2!2!) = 6 ways

so there are 10 such numbers.
So if you guess following the restriction, it would be a prob of 1/10

Answer 2

Thx!