Show that in any set of 513 social security numbers there ar

Show that in any set of 513 social security numbers, there are two that have the same placement of 0\'s (e.g., 078-43-0020 and 063-39-0050 would be such a pair).

Solution

we have to find the no using 0----9 (10 digit),we can find by 10! ways but 0 must be in same position (take 2 zero as one no so total no of digit wil be 9,they can be arranged in 9!*2! ways).wehave to find the probability that will be (9!*2!)/10! ways