Combination of excursion

Question

From a class of 25 students 10 are to be chosen for an excursion party. There are 3 students who decide that either all of them will join or none of them will join. In how many ways can the excursion party be chosen

Answer 1

If you choose those $3$ students, then you still have to choose $7$ out of $22$ students. You can do this in $\binom{22}{7}$ ways. If you do not choose those $3$ students, then you still have to choose $10$ out of $22$ students. You can do this in $\binom{22}{10}$ ways. So, the total number of ways is $$\binom{22}{7}+\binom{22}{10}$$