77. How many four-digit numbers are there in which each subsequent digit

a) is less than the previous one?

b) is greater than the previous one?
77. a) We will select any 4 digits out of ten. This can be done in $C_{10}^{4}=210$ ways. For each such quartet, there is a unique way to arrange it in descending order of digits. A n s w e r. 210.

b) Since a natural number cannot start with zero, in this case, the selection of four digits is made from nine digits. A n s w e r. $C_{9}^{4}=126$.