Question

There are 8 people on the debate team. In how many ways can the coach choose 4 members to send to competition?
70
1,680
40,320

Answer 1

have you covered binomial?

Answer 2

no

Answer 3

he has to pick 4 people out of 8

for the first choice he has 8 options, then he has 7, then he has 6 then he has 5, giving:

8 x 7 x 6 x 5

but we have repeated choices, eg picking A B C D is the same choice as B A C D

we can deal with this in the following way:

for any given choice of four people, we could have made that choice in 4 x 3 x 2 x 1
ways, so dividing by this gets us the answer.

Number of ways = (8 x 7 x 6 x 5)/(4 x 3 x 2 x 1) = 70

this method is known as binomial, the number we calculated can be written as "8C4"

which is read as "8 choose 4" , the number of ways to pick 4 objects from a set of 8 objects

the general formula for nCr is:
\[nCr = \frac{n!}{(n-r)!r!}\] where ! denotes factorial

can you work out the value of "8C3" ?

Answer 4

@Luis_Rivera you haven't taken into account repeated choices, your solution allows both the choice ABCD and ABDC

Answer 5

@hithere