Question

A class has 35 students.in how many different ways can five form a group for an activity

Answer 1

324,632 possible combinations

Explanation:

We are looking for the amount of combinations of 5 students we can have in a class of 35 students. We write this as 35_C_5. The formula for finding the number of combinations of x objects from a set of y objects is x_C_y =
`(x!)/(y!*(x - y)!)`.

Then we have:

35_C_5 =
`(35!)/(5!*(30!))`

`(1.0333148*10 ^40)/(120*2.6525286*10^32)` --- expand

`(1.0333148*10^40)/(3.1830343*10^34)` --- simplify

324,632 --- simplify

324,632 possible combinations