A group of 3 students is to be selected from a group of 12 students to take part in a class in cell biology.?

Question

a. In how many ways can this be done?
b. In how many ways can the group who will not take part
be chosen?

Answer 1

A) 12C3 = 12!/(3!*9!) = 220

B) 12C9 = 12!/(9!*3!) = 220

Surprise! Surprise! Surprise! This is true since for every choice to participate must have a group that doesn't!z

Answer 2

4 and 4

Answer 3

The number of ways that you can select three students from a group of twelve is equal to the binomial coefficient (12, 3)

( 12! ) / ( 3! )( 9! ) = 220

Similarly, you can select nine from twelve using (12, 9)

( 12! ) / ( 9! )( 3! )

which is the same value

Answer 4

draw names out of a hat
select the students with the earliest birthdays
pick your favorite 3(i dont recomend this)
pick the 3 smartest

Answer 5

a) order doesn't matter so use combinations
nCr(12,3) = 12(11)(10)/3! = 220 ways

b) the exact same answer, b/c choosing the number of winners = choosing the losers so nCr(12,3) = nCr(12,9), remember this useful fact that:

nCr(x,y) = nCr(x,x-y)

Answer 6

how many kids are in each group?

Answer 7

dont know