Question

From a group of $12$ students, $8$ are to be chosen for an excursion. There are $3$ students who decide that either of them will join or none of them will join. In how many ways can the $8$ be chosen?

Answer 1

$12$ Students

$8$ Choosen

$3⟶$ Either all $3$ go or non

If all three are going than

$5$ students have to be selected from $9$

${\Rightarrow }^9{C}_5=\frac{9\times 8\times 7\times 6}{4\times 3\times 2}=126$

If all $3$ are not going then

we need to select $8$ out of $9$

${\Rightarrow }^9{C}_8=9$

Total ways $=126+9=135$

Hence the correct answer is $135$ Ways