Total no. of students = 25 No. of students chosen for an excursion party = 10 Now 3 students decided either they are all join the party or none of them will join. When all 3 of them will join the party then we have to choose 7 more students out of 22. Then no. of ways = $\binom{22}{7}$ When all 3 of them will not join the party then we have to choose 10 students out of 22. Then the no. of ways = $\binom{22}{10}$ ∴ Required no. of ways = $\binom{22}{7} + \binom{22}{10}$.