a state has license plates with 5 alphanumerica combinations, so 26 letters and digits 0 through 9 can be used. What is possible number of combinations, with no order.
We can have:
All 5 letters or
4 Letters and 1 Number or
3 Letters and 2 Numbers or
2 Letters and 3 Numbers or
1 Letter and 5 Numbers or
All 5 numbers.
Thus, the number of combinations is $\displaystyle \binom{26}{5}+\binom{26}4\binom{10}1+\binom{26}3\b inom{10}2+\binom{26}2\binom{10}3+\binom{26}1\binom {10}4+\binom{10}5$
Does this make sense?
--Chris