# Q.10.    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 ?

S seema garhwal

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, there are two cases :

The case I: All 3 off them join.

Then, the remaining 7 students can be chosen from 22 students in $^2^2C_7$ ways.

Case II : All 3 of them do not join.

Then,10 students can be chosen from 22 students in $^2^2C_1_0$  ways.

Thus, the required number of ways for the excursion of party $=^2^2C_7+^2^2C_1_0$

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