How many $10$ letter words are there using the letters a,b,c,d,e,f if
(a) the letters in the word appear in alphabetical order?
(b) each letter occurs at least once and the letters in the word appear in alphabetical order?
My Understanding:
(a) We count all possible 10-element multisets of $$\{\infty.a, \infty.b, \infty.c, \infty.d, \infty.e, \infty.f\}$$ and for every such multiset, there is only one permutation and given us the alphabetical order. We can count these using stars-bars approcach
Is this right?
Hint: This is a direct application of stars and bars. In the first case, you can place the "bars" right next to each other, or at the beginning or the end; in the second, you need a "star" on either side of each "bar."
Can you take it from here?