From the set of integers $ 1, 2, 3, . . . , 100000% a number is selected at random. What is the probability that the sum of its digits is 8? Hint: Establish a one-to-one correspondence between the set...

From the set of integers $ 1, 2, 3, . . . , 100000% a number is selected at random. What is the probability that the sum of its digits is 8? Hint: Establish a one-to-one correspondence between the set of integers from {1, 2, . . . , 100000} the sum of whose digits is 8, and the set of possible ways 8 identical objects can be placed into 5 distinguishable cells. Then use Example 2.22.

Example 2.22

Show that the number of different ways n indistinguishable objects can be placed into k distinguishable cells is