A company produces many types of watches. The type of each
watch is indicated with a string of five characters. The two first characters are based
on uppercase alphabets, except I, O, and Q. The next three characters are three digit of
numbers ranging from 000 to 300. Determine the minimum number of watches to ensure
that at least three of them have the same type.

Question

A company produces many types of watches. The type of each
watch is indicated with a string of five characters. The two first characters are based
on uppercase alphabets, except I, O, and Q. The next three characters are three digit of
numbers ranging from 000 to 300. Determine the minimum number of watches to ensure
that at least three of them have the same type.

anonymous · Answer

if repitition is allowed then for the first two place we have 23*23 choices and for the next three character we have 4*10*10 choices hence total no is 211600
but here the watches are all of different type