Question 355687
the number of ways you can select 4 multiple choice questions out of 20 multiple choice questions is:


20! / (4!*16!) = 4845


the number of ways you can select 6 true false questions out of 10 true false questions is:


10! / (6! * 4!) = 210


The quiz can be selected 210 * 4845 = 1017450 ways


to see how this works, use much smaller number.


assume you choose 1 TF out of 3 TF (TF = true false)
asume you choose 2 MC out of 4 MC (MC = multiple choice


The number of ways you can choose 1 TF out of 3 TF is:


3! / (1! * 2!) = 3


If you let a,b,c be each of the 3 TF choices, then those ways are:


a
b
c


The number of ways you can choose 2MC out of 4 MC is:


4! / (2! * 2!) = 6


if you let 1,2,3,4 be each of the 4 MC choices, then those ways are:

1,2
1,3
1,4
2,3
2,4
3,4


Multiply 3 * 6 and you get 18 total ways.


Those ways are:


a,1,2
a,1,3
a,1,4
a,2,3
a,2,4
a,3,4
b,1,2
b,1,3
b,1,4
b,2,3
b,2,4
b,3,4
c,1,2
c,1,3
c,1,4
c,2,3
c,2,4
c,3,4


The same concept applies, just with larger numbers.


You are using the combination formula.


It is:


C[n] = c! / (x! * (n-x)!)


n is the total set of possibilities.
x is the set of possibilities you are choosing out of the total set of possibilities.


With your Multiple Choice questions:

n = 20
x = 4
(n-x) = 16


With your true false questions:


n = 10
x = 6
(n-x) = 4