Find the number of way letters a,b,c,d,e that can be arranged in 10 places without repetition, as the letter should be in alphabetical order?
Like we have ten places, _ _ _ _ _ _ _ _ _ _. Arrangements like this,
a b c d e _ _ _ _ _
a _ b c d e _ _ _ _
a _ _b c d e _ _ _ _ .
.
.
_ _ _a b _ c _ d e
_ _ _a _ _ b c d e
_ _ _ _a _ b c d e
_ _ _ _ _a b c d e.
Can't be like this, _ _ _ _ _a c b d e
Choose $5$ spots. There is only $1$ way to put them in alphabetical order. Therefore there are $\binom{10}5=252$ ways.